Problems on Trains, Boats and Streams

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  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 1

    SREENIVASA INSTITUTE OF TECHNOLOGY ANDMANAGEMENT STUDIES

    Murukambattu Post, Chittoor 517 127 (A.P)AFFILIATED TO JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY

    ANANTAPUR,

    Course materialFor

    Reasoning and Quantitative Aptitude

    Module Name: PROBLEMS ON TRAINS,BOATSAND STREAMS.

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 2

    MODULE OBJECTIVE:

    Decision making for planning, policy and management relies increasingly on thequantitative reasoning, which entails the collection, analysis and interpretation of quantitativedata. This course is designed to introduce principles and techniques to solve trains, boats andstreams related problems.

    Develop logical reasoning in a problem solving framework. One goal is to develop adisciplined logical analysis of word problems. Such reasoning is the foundation for buildingssimple mathematical models of problems-models implicit on trains, boats and streams. Howevera logical mind will serve a person well in any field.

    At the end of these course students:

    1) To be able to understand the types of formulae used to calculate trains, boats and streams.2) To be solving many problems related to trains, boats and streams which can be useful to

    students to face interviews

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 3

    PREREQUISITES:1. a km/hr= (a* 5/18) m/s.

    2. a m / s = (a*18/5) km/hr.

    3 Time taken by a train of length 1 metres to pass a pole or a standing man or a signal post isequal to the time taken by the train to cover 1 metres.

    4. Time taken by a train of length 1 metres to pass a stationary object of length b metres is thetime taken by the train to cover (1 + b) metres.

    5. Suppose two trains or two bodies are moving in the same direction at u m / s and v m/s, whereu > v, then their relatives speed = (u - v) m / s.

    6. Suppose two trains or two bodies are moving in opposite directions at u m / s and v m/s, thentheir relative speed is = (u + v) m/s.

    7. If two trains of length a metres and b metres are moving in opposite directions at u m / s and vm/s, then time taken by the trains to cross each other = (a + b)/(u+v) sec.

    8.If two trains of length a metres and b metres are moving in the same directionat u m / s and vm / s, then the time taken by the faster train to cross the slower train = (a+b)/(u-v) sec.

    9. If two trains (or bodies) start at the same time from points A and B towards each other and aftercrossing they take a and b sec in reaching B and A respectively, then

    (A's speet) : (Bs speed) = (b1/2: a1/2).

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 4

    SOLVED EXAMPLES:

    Ex.I. A train 100 m long is running at the speed of 30 km / hr. Find the time taken byit to pass a man standing near the railway line. (S.S.C. 2001)

    Sol. Speed of the train = (30 x 5/18_) m / sec = (25/3) m/ sec.

    Distance moved in passing the standing man = 100 m.

    Required time taken = 100/(25/3) = (100 *(3/25)) sec = 12 sec

    Ex. 2. A train is moving at a speed of 132 km/br. If the length of the train is110 metres, howlong will it take to cross a railway platform 165 metres long? (Bank P.O.2004)

    Sol. Speed of train = 132 *(5/18) m/sec = 110/3 m/sec.Distance covered in passing the platform = (110 + 165) m = 275 m.Time taken =275 *(3/110) sec =15/2 sec = 7 sec

    Ex. 3. A man is standing on a railway bridge which is 180 m long. He finds that atrain crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of thetrain and its speed?

    (SASKEN 2003)

    Sol. Let the length of the train be x metres,

    Then, the train covers x metres in 8 seconds and (x + 180) metres in 20 secx/8=(x+180)/20 20x = 8 (x + 180) x = 120.Length of the train = 120 m.

    Speed of the train = (120/8) m / sec = m / sec = (15 *18/5) kmph = 54 kmEx. 4. A train 150 m long is running with a speed of 68 kmph. In what time will it pass aman who is running at 8 kmph in the same direction in which the train is going?

    (WIPRO 2008)Sol: Speed of the train relative to man = (68 - 8) kmph

    = (60* 5/18) m/sec = (50/3)m/sec

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 5

    Time taken by the train to cross the man I

    = Time taken by It to cover 150 m at 50/3 m / sec = 150 *3/ 50 sec = 9sec

    Ex. 5. A train 220 m long is running with a speed of 59 kmph. In what will

    it pass a man who is running at 7 kmph in the direction opposite to that in which the trainis going?

    sol. Speed of the train relative to man = (59 + 7) kmph= 66 *5/18 m/sec = 55/3 m/sec.

    Time taken by the train to cross the man = Time taken by it to cover 220 m at (55/3) m / sec= (220 *3/55) sec = 12 secEx. 6. Two trains 137 metres and 163 metres in length are running towards each other onparallel lines, one at the rate of 42 kmph and another at 48 kmpb. In what time will theybe clear of each other from the moment they meet?

    Sol. Relative speed of the trains = (42 + 48) kmph = 90 kmph

    =(90*5/18) m / sec = 25 m /sec.

    Time taken by the trains to'pass each other

    = Time taken to cover (137 + 163) m at 25 m /sec =(300/25) sec = 12 secEx. 7. Two trains 100 metres and 120 metres long are running in the same direction withspeeds of 72 km/hr,In howmuch time will the first train cross the second? (TCS 2007)

    Sol: Relative speed of the trains = (72 - 54) km/hr = 18 km/hr

    = (18 * 5/18) m/sec = 5 m/sec.

    Time taken by the trains to cross each other

    = Time taken to cover (100 + 120) m at 5 m /sec = (220/5) sec = 44 sec.Ex. 8. A train 100 metres long takes 6 seconds to cross a man walking at 5 kmph in thedirection opposite to that of the train. Find the speed of the train.?

    Sol:Let the speed of the train be x kmph.

    Speed of the train relative to man = (x + 5) kmph = (x + 5) *5/18 m/sec.

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 6

    Therefore 100/((x+5)*5/18)=6 30 (x + 5) = 1800 x = 55Speed of the train is 55 kmph.

    Ex. 9. A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes.12 secto pass a man walking at 6 kmph in the same direction in which the train is going . Find thelength of the train and the length of the platform. (CAT 2006)Sol:Let the length of train be x metres and length of platform be y metres.

    Speed of the train relative to man = (54 - 6) kmph = 48 kmph= 48*(5/18) m/sec = 40/3 m/sec.In passing a man, the train covers its own length with relative speed.

    Length of train = (Relative speed * Time) = ( 40/3)*12 m = 160 m.

    Also, speed of the train = 54 *(5/18)m / sec = 15 m / sec.(x+y)/15 = 20 x + y = 300 Y = (300 - 160) m = 140 m.

    Ex10. A man sitting in a train which is traveling at 50 kmph observes that a goods train,traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long,find its speed.?(ACCENTURE 2008)

    Sol: Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.

    Speed of goods train = (112 - 50) kmph = 62 kmph.Ex. 11. Find the time taken by a train 180 m long, running at 72 kmph,in crossing anelectric pole.

    Sol. Speed of the train = (72 x 5/18) m/sec = 20 m/sec.Distance moved in passing the pole = 180 m.Required time taken = (180/20) sec = 9 sec.

    Ex. 12. A train 140 m long is running at 60 kmph. In how much time wiU it pass a platform260 m long?

    Sol. Speed of the train = (60 x 5/18) m/sec =50/3m/sec.Distance covered in passing the platform = (140 + 260) m = 400 m:. Time taken = (400 x 3/50) see = 24 sec.

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 7

    Ex. 13. A man is standing on a railway bridge which is 180 m long. He finds that a traincrosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train andits speed.(INFOSYS 2008)

    Sol. Let the length of the train be x metres.

    Then, the train covers x metres in 8 seconds and (x + 180) metres in 20 seconds.:. X/8 = (x + 180)/20 20x=8(x +180) x=120:. Length of train = 120m.Speed of train = (120/8) m/sec = 15 m/sec = [15 X 18/5 ] Kmph

    = 54 Kmph.

    Ex. 14. A train 150 m long is running with a speed of 68 kmph. In what time will it pass aman who is running at 8 kmph in the same direction in which the train is going ?(BANK PO 2006)

    Sol. Speed of the train relative to man = (68 - 8) kmph= (60 x 5/18)m/see = 50/3 m/sec

    Time taken by the train to cross the man = Time taken by it to cover 150 m at ( 50/3)m/sec= (150 x 3/50 )sec = 9 sec.

    Ex. 15. A train 220 m long is running with a speed of 59 kmph. In what time will it pass aman who is running at 7 kmph in the direction opposite to that in which the train is going?

    (S.S.C 2004)Sol. Speed of the train relative to man = (59 + 7) kmph

    = (66 x 5/18 ) m/sec = ( 55/3) m/sec.Time taken by the train to cross the man

    :. (x + y)/15 = 20 or x + y = 300 or y =(300 160) m = 140m.:. Length of the platform = 140 m.

    Ex. 16. A man sitting in a train which is traveling at 50 kmph observes that a goods train,traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 150 m long,find its speed.(HEXAWARE 2007)

    Sol. Relative speed = (150/9) m/sec =(150/ 9 x 18/5) kmph = 60 kmph.:. Speed of goods train = (60 - 50) kmph = 10 kmph.

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 8

    EXERCISE PROBLEMS:

    1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the lengthof the train? (CSC 2008)A. 120 metres B. 180 metres

    C. 324 metres D. 150 metresAnswer & ExplanationAnswer: Option DExplanation:

    Speed= 60 x5

    m/sec=

    50m/sec.18 3

    Length of the train = (Speed x Time) = 50 x 9m = 150 m.3

    2. A train 125 m long passes a man, running at 5 km/hr in the same direction in which thetrain is going, in 10 seconds. The speed of the train is:A. 45 km/hr B. 50 km/hr

    C. 54 km/hr D. 55 km/hrAnswer & ExplanationAnswer: Option BExplanation:

    Speed of the train relative to man =125

    m/sec10

    =

    25m/sec.2

    =

    25x

    18km/hr2 5

    = 45 km/hr.Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.

    x - 5 = 45 x = 50 km/hr.

    3. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr cancross in 30 seconds, is:(CTS 2009)A. 200 m B. 225 m

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 9

    C. 245 m D. 250 mAnswer & ExplanationAnswer: Option CExplanation:

    Speed = 45 x5

    m/sec=

    25m/sec.18 2

    Time = 30 sec.Let the length of bridge be x metres.

    Then,130 + x

    =

    2530 2

    2(130 + x) = 750x = 245 m.

    4. Two trains running in opposite directions cross a man standing on the platform in 27seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratioof their speeds is.(IBM 2008)A. 1 : 3 B. 3 : 2

    C. 3 : 4 D. None of theseAnswer & ExplanationAnswer: Option BExplanation:Let the speeds of the two trains be x m/sec and y m/sec respectively.Then, length of the first train = 27x metres,and length of the second train = 17y metres.

    27x + 17y= 23

    x+ y27x + 17y = 23x + 23y4x = 6yx

    =

    3.

    y 2

    5. A train passes a station platform in 36 seconds and a man standing on the platform in20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?A. 120 m B. 240 m

    C. 300 m D. None of theseAnswer & ExplanationAnswer: Option BExplanation:

    Speed = 54 x5

    m/sec = 15 m/sec.18Length of the train = (15 x 20)m = 300 m.

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 10

    Let the length of the platform be x metres.

    Then,x + 300

    = 1536

    x + 300 = 540x = 240 m.

    6. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform650 m long?(TCS 2006)A. 65 sec B. 89 sec

    C. 100 sec D. 150 secAnswer & ExplanationAnswer: Option BExplanation:

    Speed =240

    m/sec = 10 m/sec.24

    Required time =240 + 650 sec = 89 sec.

    7. Two trains of equal length are running on parallel lines in the same direction at 46km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The lengthof each train is:A. 50 m B. 72 m

    C. 80 m D. 82 mAnswer & ExplanationAnswer: Option AExplanation:Let the length of each train be x metres.Then, distance covered = 2x metres.Relative speed = (46 - 36) km/hr

    = 10 x5

    m/sec18

    =

    25m/sec9

    2x=

    2536 92x = 100x = 50.

    8. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge140 m long?(IGATE 2009)

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 11

    A. 40 sec B. 42 sec

    C. 45 sec D. 48 secAnswer & ExplanationAnswer: Option AExplanation:

    Formula for converting from km/hr to m/s: X km/hr = X x5

    m/s.18

    Therefore, Speed = 45 x5

    m/sec=

    25m/sec.

    18 2Total distance to be covered = (360 + 140) m = 500 m.Formula for finding Time =

    DistanceSpeed

    Required time =500 x 2

    sec= 40 sec.

    25

    9. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengthsare 1.10 km and 0.9 km respectively. The time taken by the slower train to cross thefaster train in seconds is:(PATNI 2008)A. 36 B. 45

    C. 48 D. 49Answer & ExplanationAnswer: Option CExplanation:Relative speed = (60+ 90) km/hr

    = 150 x5

    m/sec18

    =

    125m/sec.3

    Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.Required time = 2000 x

    3sec = 48 sec.125

    10. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of theengine of a 120 metres long train running at 45 kmph in the same direction. In howmuch time will the train pass the jogger?A. 3.6 sec B. 18 sec

    C. 36 sec D. 72 secAnswer & ExplanationAnswer: Option CExplanation:

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 12

    Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.= 36 x

    5m/sec18

    = 10 m/sec.Distance to be covered = (240 + 120) m = 360 m.

    Time taken =360

    sec= 36 sec.

    10

    11. A 270 metres long train running at the speed of 120 kmph crosses another trainrunning in opposite direction at the speed of 80 kmph in 9 seconds. What is the lengthof the other train?(HCL 2009)A. 230 m B. 240 m

    C. 260 m D. 320 m

    E. None of theseAnswer & ExplanationAnswer: Option AExplanation:Relative speed = (120 + 80) km/hr

    = 200 x5

    m/sec18

    =

    500m/sec.9

    Let the length of the other train be x metres.

    Then,x + 270

    =

    5009 9

    x + 270 = 500x = 230.

    12. A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26seconds. What is the length of the goods train?(CTS 2005)A. 230 m B. 240 m

    C. 260 m D. 270 mAnswer & ExplanationAnswer: Option DExplanation:

    Speed = 72 x5

    m/sec= 20 m/sec.

    18Time = 26 sec.Let the length of the train be x metres.Then, x + 250 = 20

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 13

    26x + 250 = 520x = 270.

    13. Two trains, each 100 m long, moving in opposite directions, cross each other in 8seconds. If one is moving twice as fast the other, then the speed of the faster train is:

    (CAT 2010)A. 30 km/hr B. 45 km/hr

    C. 60 km/hr D. 75 km/hrAnswer & ExplanationAnswer: Option CExplanation:Let the speed of the slower train be x m/sec.Then, speed of the faster train = 2x m/sec.Relative speed = (x + 2x) m/sec = 3x m/sec.

    (100 + 100)= 3x

    824x = 200

    x =25

    .

    3

    So, speed of the faster train =50

    m/sec3

    =

    50x

    18km/hr3 5

    = 60 km/hr.

    14. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hrrespectively in opposite directions on parallel tracks. The time (in seconds) which theytake to cross each other, is:A. 9 B. 9.6

    C. 10 D. 10.8Answer & ExplanationAnswer: Option DExplanation:

    Relative speed = (60 + 40) km/hr = 100 x 5m/sec

    =

    250m/sec.18 9

    Distance covered in crossing each other = (140 + 160) m = 300 m.Required time = 300 x

    9sec

    =

    54sec = 10.8 sec.

    250 5

    15. A train 110 metres long is running with a speed of 60 kmph. In what time will it

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 14

    pass a man who is running at 6 kmph in the direction opposite to that in which thetrain is going? (INFOSYS 2006)

    A. 5 sec B. 6 sec

    C. 7 sec D. 10 secAnswer & ExplanationAnswer: Option BExplanation:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.

    = 66 x5

    m/sec18

    =

    55m/sec.3

    Time taken to pass the man = 110 x3

    sec = 6 sec.5516.

    A train travelling at a speed of 75 mph enters a tunnel 3 miles long. The train is milelong. How long does it take for the train to pass through the tunnel from the momentthe front enters to the moment the rear emerges?A. 2.5 min B. 3 min

    C. 3.2 min D. 3.5 minAnswer & ExplanationAnswer: Option BExplanation:

    Total distance covered =7

    +1

    miles2 4

    =

    15miles.

    4

    Time taken =15

    hrs4 x 75

    =

    1hrs

    20

    =

    1x 60 min.

    20

    REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 14

    pass a man who is running at 6 kmph in the direction opposite to that in which thetrain is going? (INFOSYS 2006)

    A. 5 sec B. 6 sec

    C. 7 sec D. 10 secAnswer & ExplanationAnswer: Option BExplanation:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.

    = 66 x5

    m/sec18

    =

    55m/sec.3

    Time taken to pass the man = 110 x3

    sec = 6 sec.5516.

    A train travelling at a speed of 75 mph enters a tunnel 3 miles long. The train is milelong. How long does it take for the train to pass through the tunnel from the momentthe front enters to the moment the rear emerges?A. 2.5 min B. 3 min

    C. 3.2 min D. 3.5 minAnswer & ExplanationAnswer: Option BExplanation:

    Total distance covered =7

    +1

    miles2 4

    =

    15miles.

    4

    Time taken =15

    hrs4 x 75

    =

    1hrs

    20

    =

    1x 60 min.

    20

    REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 14

    pass a man who is running at 6 kmph in the direction opposite to that in which thetrain is going? (INFOSYS 2006)

    A. 5 sec B. 6 sec

    C. 7 sec D. 10 secAnswer & ExplanationAnswer: Option BExplanation:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.

    = 66 x5

    m/sec18

    =

    55m/sec.3

    Time taken to pass the man = 110 x3

    sec = 6 sec.5516.

    A train travelling at a speed of 75 mph enters a tunnel 3 miles long. The train is milelong. How long does it take for the train to pass through the tunnel from the momentthe front enters to the moment the rear emerges?A. 2.5 min B. 3 min

    C. 3.2 min D. 3.5 minAnswer & ExplanationAnswer: Option BExplanation:

    Total distance covered =7

    +1

    miles2 4

    =

    15miles.

    4

    Time taken =15

    hrs4 x 75

    =

    1hrs

    20

    =

    1x 60 min.

    20

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 15

    = 3 min.

    17. A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1minute, then the length of the tunnel (in meters) is.(BANK PO 2009)A. 130 B. 360

    C. 500 D. 540Answer & ExplanationAnswer: Option CExplanation:

    Speed = 78 x5

    m/sec =65

    m/sec.18 3

    Time = 1 minute = 60 seconds.Let the length of the tunnel be x metres.

    Then,800 + x

    =

    6560 3

    3(800 + x) = 3900x = 500.

    18. A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in18 seconds. What is the length of the platform?A. 320 m B. 350 m

    C. 650 m D. Data inadequateAnswer & ExplanationAnswer: Option BExplanation:

    Speed =300

    m/sec =50

    m/sec.18 3

    Let the length of the platform be x metres.

    Then,x + 300

    =

    5039 3

    3(x + 300) = 1950x = 350 m.

    19. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Itslength is:A. 50 m B. 150 m

    C. 200 m D. Data inadequateAnswer & ExplanationAnswer: Option BExplanation:

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 16

    Let the length of the train be x metres and its speed by y m/sec.

    Then,x

    = 15 y =x

    .

    y 15x + 100

    =

    x

    25 1515(x + 100) = 25x15x + 1500 = 25x1500 = 10xx = 150 m.

    20. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20seconds respectively. What is the speed of the train?(S.B.I PO 2006)A. 69.5 km/hr B. 70 km/hr

    C. 79 km/hr D. 79.2 km/hrAnswer & ExplanationAnswer: Option DExplanation:Let the length of the train be x metres and its speed by y m/sec.

    Then,x

    = 8 x = 8yy

    Now,x + 264

    = y20

    8y + 264 = 20yy = 22.

    Speed = 22 m/sec = 22 x18

    km/hr = 79.2 km/hr.5

    21. How many seconds will a 500 metre long train take to cross a man walking with a speedof 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?A. 25 B. 30

    C. 40 D. 45Answer & ExplanationAnswer: Option BExplanation:Speed of the train relative to man = (63 - 3) km/hr

    = 60 km/hr

    = 60 x5

    m/sec18

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 17

    =

    50m/sec.

    3

    Time taken to pass the man = 500 x3

    sec50

    = 30 sec.

    22. Two goods train each 500 m long, are running in opposite directions on parallel tracks.Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slowertrain to pass the driver of the faster one.(CAT 2009)A. 12 sec B. 24 sec

    C. 48 sec D. 60 secAnswer & ExplanationAnswer: Option BExplanation:Relative speed = = (45 + 30) km/hr

    = 75 x5

    m/sec18

    =

    125m/sec.

    6

    We have to find the time taken by the slower train to pass the DRIVER of the faster train andnot the complete train.So, distance covered = Length of the slower train.Therefore, Distance covered = 500 m.

    Required time = 500 x6

    = 24 sec.125

    23. Two trains are running in opposite directions with the same speed. If the length of eachtrain is 120 metres and they cross each other in 12 seconds, then the speed of each train(in km/hr) is:A. 10 B. 18

    C. 36 D. 72Answer & ExplanationAnswer: Option CExplanation:Let the speed of each train be x m/sec.Then, relative speed of the two trains = 2x m/sec.

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 18

    So, 2x =(120 + 120)12

    2x = 20x = 10.

    Speed of each train = 10 m/sec = 10 x18

    km/hr = 36 km/hr.5

    24. Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross atelegraph post. If the length of each train be 120 metres, in what time (in seconds) willthey cross each other travelling in opposite direction?A. 10 B. 12

    C. 15 D. 20Answer & ExplanationAnswer: Option BExplanation:

    Speed of the first train =120

    m/sec = 12 m/sec.10

    Speed of the second train =120

    m/sec = 8 m/sec.15

    Relative speed = (12 + 8) = 20 m/sec.Required time =

    (120 + 120)sec = 12 sec.

    20

    25. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long comingfrom opposite direction in 6 seconds. The speed of the second train is:A. 48 km/hr B. 54 km/hr

    C. 66 km/hr D. 82 km/hrAnswer & ExplanationAnswer: Option DExplanation:Let the speed of the second train be x km/hr.Relative speed = (x + 50) km/hr

    = (x + 50) x 5 m/sec18

    =

    250 + 5xm/sec.

    18

    Distance covered = (108 + 112) = 220 m.220

    = 6250 + 5x

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 19

    18250 + 5x = 660x = 82 km/hr.

    26. Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction.Fast train completely passes a man sitting in the slower train in 5 seconds. What is thelength of the fast train?

    A. 23 m B. 232

    m9

    C. 277

    m9

    D. 29 m

    Answer & ExplanationAnswer: Option CExplanation:

    Relative speed = (40 - 20) km/hr = 20 x 5 m/sec = 50 m/sec.18 9

    Length of faster train =50

    x 5 m =250

    m = 277

    m.9 9 9

    27. A train overtakes two persons who are walking in the same direction in which the trainis going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10seconds respectively. The length of the train is:(S.S.C 2005)A. 45 m B. 50 m

    C. 54 m D. 72 mAnswer & ExplanationAnswer: Option BExplanation:

    2 kmph = 2 x5

    m/sec =5

    m/sec.18 9

    4 kmph = 4 x5

    m/sec =10

    m/sec.18 9

    Let the length of the train be x metres and its speed by y m/sec.

    Then,x

    = 9 andx

    = 10.y -

    59

    y -109

    9y - 5 = x and 10(9y - 10) = 9x9y - x = 5 and 90y - 9x = 100.

    On solving, we get: x = 50.Length of the train is 50 m.

    28. A train overtakes two persons walking along a railway track. The first one walks at 4.5km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 20

    respectively to overtake them. What is the speed of the train if both the persons arewalking in the same direction as the train?A. 66 km/hr B. 72 km/hr

    C. 78 km/hr D. 81 km/hrAnswer & ExplanationAnswer: Option DExplanation:

    4.5 km/hr = 4.5 x5

    m/sec =5

    m/sec = 1.25 m/sec, and18 4

    5.4 km/hr = 5.4 x5

    m/sec =3

    m/sec = 1.5 m/sec.18 2

    Let the speed of the train be x m/sec.Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5

    8.4x - 10.5 = 8.5x - 12.750.1x = 2.25x = 22.5

    Speed of the train = 22.5 x18

    km/hr = 81 km/hr.5

    29. A train travelling at 48 kmph completely crosses another train having half its lengthand travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railwayplatform in 45 seconds. The length of the platform isA. 400 m B. 450 m

    C. 560 m D. 600 mAnswer & ExplanationAnswer: Option AExplanation:Let the length of the first train be x metres.

    Then, the length of the second train isx

    metres.2

    Relative speed = (48 + 42) kmph = 90 x 5 m/sec = 25 m/sec.18

    [x + (x/2)]= 12 or

    3x= 300 or x = 200.

    25 2Length of first train = 200 m.

    Let the length of platform be y metres.

    Speed of the first train = 48 x5

    m/sec =40

    m/sec.18 3

    (200 + y) x 3 = 4540

    600 + 3y = 1800

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 21

    y = 400 m

    30. Two stations A and B are 110 km apart on a staright line. One train starts from A at 7a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. andtravels towards A at a speed of 25 kmph. At what time will they meet?(ACCENTURE 2007)A. 9 a.m. B. 10 a.m.

    C. 10.30 a.m. D. 11 a.m.Answer & ExplanationAnswer: Option BExplanation:Suppose they meet x hours after 7 a.m.Distance covered by A in x hours = 20x km.Distance covered by B in (x - 1) hours = 25(x - 1) km.

    20x + 25(x - 1) = 11045x = 135x = 3.

    So, they meet at 10 a.m.

    31. Two, trains, one from Howrah to Patna and the other from Patna to Howrah, startsimultaneously. After they meet, the trains reach their destinations after 9 hours and 16hours respectively. The ratio of their speeds is:(IBM 2006)A. 2 : 3 B. 4 : 3

    C. 6 : 7 D. 9 : 16Answer & ExplanationAnswer: Option BExplanation:Let us name the trains as A and B. Then,(A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3.

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 22

    QUESTION BANK:1. A train moves with a speed of t 08 kmph. Its speed in meters per second is :(a) 38.8 (b) 18 (c) 30

    2. A speed of 14 meters per second is the same as :

    (a) 50.4 km/Hr (b) 28 km/hr (c) 70 km/hr (d) 46.6 km/hr

    3. A man on riding crosses a bridge in 5 minutes when riding is being done at 15 kmph. The.length of the bridge is :

    (a) 125 m (b) 250 m (c) 1250 m (d) 2500 m

    4. A train 150 m long is running at a speed of 90 kmph. Time taken by the train to cross a tree is :

    (a) 3 see (b) 4 see (c) 6 see (d) 8 see

    5. A train 280 m long, running with a speed of 63 kmIhr will pass an electric pole in :.

    (a) 20 see (b) 16 see (c) 15 sec (d) 18 sec

    6. A train is moving at a speed of 132 kmph. If the length of the train is 110 meters, how longwill it take to cross a railway platform 165 m . long?

    (a) 5 see (b) 7.5 see (c) 10 see (d) 15 sec

    7. A train 280 m long is moving at 60 kmph. The time taken by the train to cross a tunnel 220 mlong, is :

    (a) 20 sec (b). 25sec (c) 30 sec (d) 35 sec

    8.With a speed of 60 kmph a train crosses a pole in 30 seconds. The length of the train is :

    (a) 1000 m (b) 900 m (c) 750 m (d) 500 m

    9. A train traveling at a speed of 90 kmph, crosses a pole in 10 seconds. The length of the trainis:a) 250 m (b) 150 m. (c) 900 m (d) 100 m

    10. A train 120 m long crosses a standing man in 15 seconds. The speed of the train is :

    (a) 32 km/hr (b) 36.5 km/hr (c) 28.8 km/hr (d) 40 km/hr

    11. A train 700 m long is running at 72 kmph. If it crosses a tunnel in 1 minute, the length of thetunnel is :

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 23

    (a) 700 m (b) 600 m (c) 550 m (d) 500 m

    12. The length of a bridge which a train 130 m long and traveling at 45 kmph can cross in 30seconds, is :

    (a) 200 m (b) 225 m (c) 245 m (d) 250 m

    13. If a 200 m long train crosses a platform of the same length as that of the train in 20 seconds,then the speed of the train is:

    (a) 50 km/hr (b) 60 km/hr (c) 72 km/hr (d) 80 km/hr

    14. A train 60 m long passes a platform 90 m long in 10 seconds. The speed of the train is :

    (a)'10 km/hr (b) 15 km/hr (c) 54 km/hr (d) 48 km/hr

    15. A train 300 m long crossed a platform 900 m long in 1 minute 12 seconds. The speed of thetrain (in km/hr) is :

    (a) 45 (b) 50 (c) 54 (d) 60

    16. A train crosses a platform 100 m long in 60 seconds at a speed of 45 kmph. The time takenby the train to cross an electric pole is :

    (a) 8 sec (b) 52 sec (c) 1 minute (d) data inadequate

    17. A train of length 150 m takes 40.5 seconds to cross a tunnel of length 300 m. The speed ofthe train (in km/hr) is :

    (a) 13.33 (b) 26.67 (c) 40 (d) 400

    18. A .train 150 m long takes 20 seconds to cross a platform 450 m long. The speed of the train(in m/sec) is :

    (a) 22.5 (b) 30 (c) 45 (d) 96

    19. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its lengthis :

    (a) 200 m (b) 150 m (c) 50 m (d) data inadequate

    20. A train takes 18 seconds to pass completely through a station 162 m long and 15 secondsthrough another station 120 m long. The length of the train is :

    (a) 70 m (b) 80 m (c) 90 m (d) 100 m

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 24

    21. If a train 110 m long passes a telegraph pole in 3 seconds, then the time taken by it to cross arailway platform 165 m long, is

    (a) 3 sec (b) 4 sec (c) 5 sec (d) 7.5 sec

    22. A train 110 m long is traveling at a speed of 58 kmph. The time in which it will pass a passerby, walking at 4 kmph in the same direction,is :

    (a) 6 sec (b) 7 sec (c) 7 1/3 see (d) 7 1/3 min

    23. A train 150 m long moving at a speed of 25 meters per second overtakes a man moving at 5meters/see in opposite direction. The train will pass, the man in :

    (a) 5 sec (b) 6 see (c) 4 2/7 sec (d) 8 see

    24. Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45kmph respectively. In how much time will they cross each other, if they are running in the samedirection?

    (a) 72 sec (b) 132 sec (c) 192 sec (d) 252 see

    25. Two trains 126 m and 114 m long are running in opposite directions, one at the rate of 30kmph and another one at 42 kmph. From the moment they meet will cross each other in :

    (a) 10 sec (b) 11 sec (c) 12 sec (d) 13 sec

    26. A train 270 m long is moving at a speed of 24 kmph. It will cross a man coming from theopposite direction at a speed of 3 kmph, in :

    (a) 24 sec (b) 28 sec (c) 32 see (d) 36 sec

    27. A train 125 m long passes a man, running at 5 kmph in the same direction in which the trainis going, in 10 seconds. The speed of the train is :

    (a) 50 km/hr (b) 45 km/hr (c) 55 km/hr (d) 54 km/hr

    28. A train 11 0 m long passes a man, running at 6 kmph in the direction opposite to that of thetrain, in 6 seconds. The speed of the train is :

    (a) 60 km/hr (b) 66 km/hr (c) 54 km/hr (d) 72 km/hr

    29. Two trains are moving in the same direction at 65 kmph and 45 kmph. The faster traincrosses a man in slower train in 18 seconds. The length of the faster train is: .

    (a) 120 m (b) 180 rn (c) 100 m (d) 145 m

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 25

    30. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming fromopposite direction in 6 seconds. The speed of the second train is :

    (a) 48 kmph (b) 54kmph (c) 66 kmph (d) 82 kmph

    31. A train B speeding with 120 kmph crosses another train C, running in the same direction in 2minutes. If the lengths of the trains B and C be 100 m and 200 m respectively, what is the speedof the train C?

    (a). 111 kmph (b) 127 kmph (c) 123 kmph (d) 129 kmph

    32. Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slowertrain passes the fasten train in 8 seconds. The length of the faster train is :

    (a) 80 m (b) 100 m (c) 120 m (d) 180 m

    33. The length of a running train A is 30% more than the length of another train B running in theopposite direction. To find out the speed of the train B, which of the following information givenin statementsP and Q is sufficient?P : The speed of train A is 80 kmph.Q : They took 90 seconds to cross each other.(a) Either P or Q is sufficient (b) Both P and Q are not sufficient(c) Only Q is sufficient (d) Both P and Q are needed

    34. The speed of a 100 m long running train A is 40% more than the speed of another 180 m longtrain B running in the opposite directions. To find out the speed of train B, which of theinformation given in statements P and Q is sufficient?P : The two trains crossed each other in 6 seconds.Q : The difference between the speeds of the two trains was 26 kmph.

    (a) Only P is sufficient (b) Only Q is sufficient(c) Both P and Q are needed (d) Both P & Q are not sufficient

    35. A train running at certain speed crosses a stationary engine in 20 seconds. To find out thespeed of the train, which of the following information is necessary:(a) Only the length of the train(b) Only the length of the engine(c) Either the length of the train or the length of the engine(.d) Both the length of the train and the length of the engine

    36.' A train overtakes two persons who are walking in the same direction in which the train isgoing, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 secondsrespectively. The length of the train is :

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 26

    (a) 72 m (b) 54 m (c) 50 m (d) 45 m

    37. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m.and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A ata speed of 25 kmph. At what time will they meet?

    (a) 9 a.m. (b) 10 a.m. (c) 11 a.m. (d) 10.30 a.m.

    38. A train X starts from Meerut at 4 P.M. and reaches Ghaziabad at 5 P.M. while another trainY starts from Ghaziabad at 4 P.M. and reaches Meerut, at 5.30 PM. The two trains will crosseach other at :

    (a) 4.36 p.m. (b) 4.42 p.m. (c) 4.48 p.m. (d) 4.50 p.m.

    39. Two trains running in the same direction at 65 kmph and 47 kmph, completely pass oneanother in 1 minute. If the length of the first train is 125 m, the length of the second train is :

    (a) 125 m " (b) 150 m' (c) 175 m (d) 200 m

    40. Two' trains are running in opposite directions towards each other with speeds of 54 kmph and48 kmph respectively. If the length of one train is 250 m and they cross each other in 18 seconds,the length of the other train is :

    (a) 145 m (b) 230 m (c) 260 m (d) 180 m

    41. A train 150 m long passes a km stone in 15 seconds and another train of the same lengthtravelling in opposite direction in 8 seconds. The speed of the second train is :

    (a) 60 kmph (b) 72 kmph (c) 66 kmph (d) 99 kmph

    42. A train traveling at 48 kmph completely crosses another train having half its length andtraveling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45seconds. The length of the platform is :

    (a) 560 m (b) 400 m (c) 600 m (d) 450 m

    43. A train is running at the rate of 60 kmph. A man is also going in the same direction on a trackparallel to the rails at a speed of 45 kmph. If the train crosses the man in 48 seconds, the lengthof the train is :

    (a) 50 m (b) 100 m (c) 150 m (d) 200 m

    44 A train of length 150 m takes 10 seconds to pass over another train 100 m long coming fromthe opposite direction. If the speed of the first train be 30 kmph, the speed of the second train is :

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 27

    (a) 36 kmph (b) 54 kmph (c) 60 kmph (d) 72 kmph

    45. A man sees a train passing over a bridge 1 km long. The length of the train is half that of thebridge. If the train clears the bridge in 2 minutes, the speed of the train is :

    (a) 30 km/hr (b) 45 km/hr (c) 50 km/hr (d) 60 km/hr

    ANSWERS1. (c) 2. (a) 3. (c) 4. (c) 5. (b) 6. (b) 7. (c) 8. (d) 9. (a) 10. (c)

    11. (d) 12. (c) 13. (c) 14. (c) 15. (d) 16. (b) 17. (c) 18. (b) 19. (b) 20. (c)

    21. (d) 22 (c) 23. (a) 24. (d) 25. (c) 26. (d) 27. (a) 28. (a) 29. (c) 30. (d)

    31. (a) 32. (d) 33. (b) 34. (a) 35. (d) 36. (c) 37. (b) 38. (a) 39. (c) 40. (c)

    41. (d) 42. (b) 43. (d) 44. (c) 45. (b)

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 28

    PROBLEMS ON BOATS AND STREAMS

    PREREQUISITES:1.In water ,the direction along the stream is called downstream and ,the direction against thestream is called upstream.

    2.If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr,then:

    speed downstream=(u+v)km/hr.speed upstream=(u-v)km/hr.

    3.If the speed downstream is a km/hr and the speed upstream is b km/hr,then :

    speed in still water=1/2(a+b)km/hr

    rate of stream=1/2(a-b)km/hrSOLVED EXAMPLES:

    EX.1.A man can row upstream at 7 kmph and downstream at 10kmph.find mans rate instill water and the rate of current.

    Sol. Rate in still water=1/2(10+7)km/hr=8.5 km/hr.

    Rate of current=1/2(10-7)km/hr=1.5 km/hr.

    EX.2. A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and2hours30minutes to cover a distance of 5km upstream. find the speed of the river currentin km/hr.Sol. rate downstream=(15/3 )km/hr=(15*4/15)km/hr=4km/hr.

    Rate upstream=(5/2 )km/hr=(5*2/5)km/hr=2km/hr.

    Speed of current=1/2(4-2)km/hr=1km/hr

    EX.3. a man can row 18 kmph in still water.it takes him thrice as long to row up as to rowdown the river.find the rate of stream.

    Sol. Let mans rate upstream be x kmph.then ,his rate downstream=3xkmph.

    So,2x=18 or x=9.

    Rate upstream=9 km/hr,rate downstream=27 km/hr.

    Hence,rate of stream=1/2(27-9)km/hr=9 km/hr.

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 29

    EX.4. there is a road beside a river.two friends started from a place A,moved to a templesituated at another place B and then returned to A again.one of them moves on a cycle at aspeed of 12 km/hr,while the other sails on a boat at a speed of 10 km/hr.if the river flows atthe speed of 4 km/hr,which of the two friends will return to placeA first?Sol. Clearly the cyclist moves both ways at a speed of 12 km/hr.

    The boat sailor moves downstream @ (10+4)i.e.,14 km/hr and upstream @ (10-4)i.e., 6km/hr.

    So,average speed of the boat sailor=(2*14*6/14+6)km/hr

    =42/5 km/hr=8.4 km/hr.

    since the average speed of the cyclist is greater ,he will return ta A first.

    EX.5. A man can row 7 kmph in still water.if in a river running at 1.5 km/hr an hour,ittakes him 50 minutes to row to a place and back,how far off is the place?

    Sol. Speed downstream =(7.5+1.5)km/hr=9 km/hr;

    Speed upstream=(7.5-1.5)kmph=6kmph.

    Let the required distance be x km.then,

    x/9+x/6=50/60.

    2x+3x=(5/6*18)

    5x=15

    x=3.

    Hence,the required distance is 3km.

    EX.6. In a stream running at 2kmph,a motar boat goes 6km upstream and back again tothe starting point in 33 minutes.find the speed of the motarboat in still water.

    Sol.let the speed of the motarboat in still water be x kmph.then,

    6/x+2 +6/x-2=33/60

    11x2-240x-44=0

    11x2-242x+2x-44=0

    (x-22)(11x+2)=0

    x=22.

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 30

    EX.7.A man can row 40km upstream and 55km downstream in 13 hours also, he can row30km upstream and 44km downstream in 10 hours.find the speed of the man in still waterand the speed of the current.

    Sol.let rate upstream=x km/hr and rate downstream=y km/hr.

    Then,40/x +55/y =13(i) and 30/x +44/y =10

    Multiplying (ii) by 4 and (i) by 3 and subtracting ,we get:11/y=1 or y=11.

    Substituting y=11 in (i),we get:x=5.

    Rate in still water =1/2(11+5)kmph=8kmph.

    Rate of current=1/2(11-5)kmph=3kmph

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 31

    EXERCISE PROBLEMS:

    1. A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4km/hr, find the time taken by the boat to go 68 km downstream. (WIPRO 2007)

    A. 2 hours B. 3 hours

    C. 4 hours D. 5 hours

    Answer & Explanation

    Answer: Option C

    Explanation:

    Speed downstream = (13 + 4) km/hr = 17 km/hr.

    Time taken to travel 68 km downstream =68

    hrs = 4 hrs.17

    2. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr.The man's speed against the current is: (IGATE 2009)

    A. 8.5 km/hr B. 9 km/hr

    C. 10 km/hr D. 12.5 km/hr

    Answer & Explanation

    Answer: Option C

    Explanation:

    Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.

    Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.

    3. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while ittakes 4 hours to cover the same distance running downstream. What is the ratiobetween the speed of the boat and speed of the water current respectively?(TCS 2004)

    A. 2 : 1 B. 3 : 2

    C. 8 : 3 D. Cannot be determined

    E. None of these

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 32

    Answer & Explanation

    Answer: Option C

    Explanation:

    Let the man's rate upstream be x kmph and that downstream be y kmph.

    Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

    x x 84

    = (y x 4)5

    44x =4y

    5

    y =11

    x.5

    Required ratio =y + x

    :y - x

    2 2

    =

    16xx

    1:

    6xx

    15 2 5 2

    =

    8:

    35 5

    = 8 : 3

    4. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comesback in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

    A. 4 B. 5

    C. 6 D. 10

    Answer: Option B

    Explanation:

    Let the speed of the stream be x km/hr. Then,

    Speed downstream = (15 + x) km/hr,

    Speed upstream = (15 - x) km/hr.

    30+

    30= 4

    1(15 + x) (15 - x) 2

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 33

    900=

    9225 - x2 2

    9x2 = 225

    x2

    = 25

    x = 5 km/hr.

    5. In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream.The speed of the boat in still water (in km/hr) is.(HCL 2008)

    A. 3 km/hr B. 5 km/hr

    C. 8 km/hr D. 9 km/hr

    Answer & Explanation

    Answer: Option C

    Explanation:

    Speed in still water =1(11 + 5) kmph = 8 kmph.2

    6. A boat running downstream covers a distance of 16 km in 2 hours while for coveringthe same distance upstream, it takes 4 hours. What is the speed of the boat in stillwater?

    A. 4 km/hr B. 6 km/hr

    C. 8 km/hr D. Data inadequate

    Answer & Explanation

    Answer: Option B

    Explanation:

    Rate downstream =16

    kmph = 8 kmph.2

    Rate upstream =16

    kmph = 4 kmph.4

    Speed in still water =1(8 + 4) kmph = 6 kmph.2

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 34

    7. The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. Thedistance travelled downstream in 12 minutes is:

    A. 1.2 km B. 1.8 km

    C. 2.4 km D. 3.6 km

    Answer & Explanation

    Answer: Option D

    Explanation:

    Speed downstream = (15 + 3) kmph = 18 kmph.

    Distance travelled = 18 x12

    km = 3.6 km.60

    8. A boat takes 90 minutes less to travel 36 miles downstream than to travel the samedistance upstream. If the speed of the boat in still water is 10 mph, the speed of thestream is:(ACCENTURE 2007)

    A. 2 mph B. 2.5 mph

    C. 3 mph D. 4 mph

    Answer & Explanation

    Answer: Option A

    Explanation:

    Let the speed of the stream x mph. Then,

    Speed downstream = (10 + x) mph,

    Speed upstream = (10 - x) mph.

    36-

    36=

    90(10 - x) (10 + x) 60

    72x x 60 = 90 (100 - x2)

    x2 + 48x - 100 = 0

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 35

    (x+ 50)(x - 2) = 0

    x = 2 mph.

    9. A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takeshim 1 hour to row to a place and come back, how far is the place?

    A. 2.4 km B. 2.5 km

    C. 3 km D. 3.6 km

    Answer & Explanation

    Answer: Option A

    Explanation:

    Speed downstream = (5 + 1) kmph = 6 kmph.

    Speed upstream = (5 - 1) kmph = 4 kmph.

    Let the required distance be x km.

    Then,x

    +x

    = 16 4

    2x + 3x = 12

    5x = 12

    x = 2.4 km.

    10.A boat covers a certain distance downstream in 1 hour, while it comes back in 1 hours.If the speed of the stream be 3 kmph, what is the speed of the boat in still water?

    A. 12 kmph B. 13 kmph

    C. 14 kmph D. 15 kmph

    E. None of these

    Answer & Explanation

    Answer: Option D

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 36

    Explanation:

    Let the speed of the boat in still water be x kmph. Then,

    Speed downstream = (x + 3) kmph,

    Speed upstream = (x - 3) kmph.

    (x + 3) x 1 = (x - 3) x 32

    2x + 6 = 3x - 9

    x = 15 kmph.11. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along

    the current in 10 minutes. How long will it take to go 5 km in stationary water?(CSC 2008)

    A. 40 minutes B. 1 hour

    C. 1 hr 15 min D. 1 hr 30 min

    Answer & Explanation

    Answer: Option C

    Explanation:

    Rate downstream =1

    x 60km/hr = 6 km/hr.10

    Rate upstream = 2 km/hr.

    Speed in still water =1(6 + 2) km/hr = 4 km/hr.2

    Required time =5

    hrs = 11

    hrs = 1 hr 15 min.4 4

    12.A man can row three-quarters of a kilometre against the stream in 11 minutes and

    down the stream in 7 minutes. The speed (in km/hr) of the man in still water is:

    (SBI P.O 2001)A. 2 B. 3

    REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 36

    Explanation:

    Let the speed of the boat in still water be x kmph. Then,

    Speed downstream = (x + 3) kmph,

    Speed upstream = (x - 3) kmph.

    (x + 3) x 1 = (x - 3) x 32

    2x + 6 = 3x - 9

    x = 15 kmph.11. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along

    the current in 10 minutes. How long will it take to go 5 km in stationary water?(CSC 2008)

    A. 40 minutes B. 1 hour

    C. 1 hr 15 min D. 1 hr 30 min

    Answer & Explanation

    Answer: Option C

    Explanation:

    Rate downstream =1

    x 60km/hr = 6 km/hr.10

    Rate upstream = 2 km/hr.

    Speed in still water =1(6 + 2) km/hr = 4 km/hr.2

    Required time =5

    hrs = 11

    hrs = 1 hr 15 min.4 4

    12.A man can row three-quarters of a kilometre against the stream in 11 minutes and

    down the stream in 7 minutes. The speed (in km/hr) of the man in still water is:

    (SBI P.O 2001)A. 2 B. 3

    REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 36

    Explanation:

    Let the speed of the boat in still water be x kmph. Then,

    Speed downstream = (x + 3) kmph,

    Speed upstream = (x - 3) kmph.

    (x + 3) x 1 = (x - 3) x 32

    2x + 6 = 3x - 9

    x = 15 kmph.11. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along

    the current in 10 minutes. How long will it take to go 5 km in stationary water?(CSC 2008)

    A. 40 minutes B. 1 hour

    C. 1 hr 15 min D. 1 hr 30 min

    Answer & Explanation

    Answer: Option C

    Explanation:

    Rate downstream =1

    x 60km/hr = 6 km/hr.10

    Rate upstream = 2 km/hr.

    Speed in still water =1(6 + 2) km/hr = 4 km/hr.2

    Required time =5

    hrs = 11

    hrs = 1 hr 15 min.4 4

    12.A man can row three-quarters of a kilometre against the stream in 11 minutes and

    down the stream in 7 minutes. The speed (in km/hr) of the man in still water is:

    (SBI P.O 2001)A. 2 B. 3

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 37

    C. 4 D. 5

    Answer: Option D

    Explanation:

    We can write three-quarters of a kilometre as 750 metres,

    and 11 minutes as 675 seconds.

    Rate upstream =750

    m/sec=

    10m/sec.

    675 9

    Rate downstream =750

    m/sec=

    5m/sec.

    450 3

    Rate in still water =1 10

    +5

    m/sec2 9 3

    =

    25m/sec

    18

    =

    25x

    18km/hr18 5

    = 5 km/hr.

    13. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. Aman rows to a place at a distance of 105 km and comes back to the starting point. Thetotal time taken by him is.(S.S.C 2005)

    A. 16 hours B. 18 hours

    C. 20 hours D. 24 hours

    Answer & Explanation

    Answer: Option D

    Explanation:

    Speed upstream = 7.5 kmph.

    Speed downstream = 10.5 kmph.

    Total time taken =105

    +105

    hours = 24 hours.7.5 10.5

    REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 37

    C. 4 D. 5

    Answer: Option D

    Explanation:

    We can write three-quarters of a kilometre as 750 metres,

    and 11 minutes as 675 seconds.

    Rate upstream =750

    m/sec=

    10m/sec.

    675 9

    Rate downstream =750

    m/sec=

    5m/sec.

    450 3

    Rate in still water =1 10

    +5

    m/sec2 9 3

    =

    25m/sec

    18

    =

    25x

    18km/hr18 5

    = 5 km/hr.

    13. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. Aman rows to a place at a distance of 105 km and comes back to the starting point. Thetotal time taken by him is.(S.S.C 2005)

    A. 16 hours B. 18 hours

    C. 20 hours D. 24 hours

    Answer & Explanation

    Answer: Option D

    Explanation:

    Speed upstream = 7.5 kmph.

    Speed downstream = 10.5 kmph.

    Total time taken =105

    +105

    hours = 24 hours.7.5 10.5

    REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 37

    C. 4 D. 5

    Answer: Option D

    Explanation:

    We can write three-quarters of a kilometre as 750 metres,

    and 11 minutes as 675 seconds.

    Rate upstream =750

    m/sec=

    10m/sec.

    675 9

    Rate downstream =750

    m/sec=

    5m/sec.

    450 3

    Rate in still water =1 10

    +5

    m/sec2 9 3

    =

    25m/sec

    18

    =

    25x

    18km/hr18 5

    = 5 km/hr.

    13. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. Aman rows to a place at a distance of 105 km and comes back to the starting point. Thetotal time taken by him is.(S.S.C 2005)

    A. 16 hours B. 18 hours

    C. 20 hours D. 24 hours

    Answer & Explanation

    Answer: Option D

    Explanation:

    Speed upstream = 7.5 kmph.

    Speed downstream = 10.5 kmph.

    Total time taken =105

    +105

    hours = 24 hours.7.5 10.5

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 38

    14. A man takes twice as long to row a distance against the stream as to row the samedistance in favour of the stream. The ratio of the speed of the boat (in still water) andthe stream is:

    A. 2 : 1 B. 3 : 1

    C. 3 : 2 D. 4 : 3

    Answer & Explanation

    Answer: Option B

    Explanation:

    Let man's rate upstream be x kmph.

    Then, his rate downstream = 2x kmph.

    (Speed in still water) : (Speed of stream) = 2x + x : 2x - x2 2

    =

    3x:

    x

    2 2

    = 3 : 1.

    15. A man rows to a place 48 km distant and come back in 14 hours. He finds that he canrow 4 km with the stream in the same time as 3 km against the stream. The rate of thestream is.(BANK PO 2008)

    A. 1 km/hr B. 1.5 km/hr

    C. 2 km/hr D. 2.5 km/hr

    Answer: Option A

    Explanation:

    Suppose he move 4 km downstream in x hours. Then,

    Speed downstream =4

    km/hr.x

    Speed upstream =3

    km/hr.x

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 39

    48+

    48= 14 or x =

    1.(4/x) (3/x) 2

    So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.

    Rate of the stream =1(8 - 6) km/hr = 1 km/hr.2

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 40

    QUESTION BANK:

    1. If a man can swim downstream at 6 kmph and upstream at 2 kmph, his speed in still water'is :(a) 4 km/hr (b) 2 km/hr (c) 3 km/hr (d) 2.5 km/hr

    2. A man can row upstream at 8 kmph and downstream at 13 kmph. The speed of the stream is :(a) 5 km/hr (b) 2.5 km/hr (c) 10.5 km/hr (d) 4.2 km/hr

    3. If Anshul rows 15 km upstream and 21 km downstream taking 3 hours each time, then thespeed of the stream is :(a) 1 km/hr (b) 1.5 km/hr (c) 2 km/hr (d) 12 km/hr

    4. A man rows 750 m in 675 seconds against the stream and returns in 7 minutes. His rowingspeed in still water is:(a) 3 km/hr (b) 4 km/hr (c) 5 km/hr (d) 6 km/hr

    5. A man rows 13 km upstream in 5 hours and also 28 km downstream in 5 hours. The velocityof the stream is :(a) 1.5 km/hr (b) 2 km/hr ( c) 2.5 km/hr (d) 3 km/hr

    6. If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph, then thespeed of the boat in still water is:(a) 4.2 km/hr (b) 9 km/hr (c) 13 km/hr (d) 21 km/hr

    7. A man can row 9 1/3 kmph in still water and finds that it takes him thrice as much time to rowup than as to row down the same distance in the river. The speed of the current is :(a) 3 1/3 km/hr (b) 3 1/9 km/hr (c) 4 2/3 km/hr (d) 14 km/hr

    8. A man can row a boat at 10 kmph in still water. If the speed of the stream is 6 kmph, the timetaken to row a distance of 80 km down the stream is :(a) 8 hours (b) 5 hours (c) 10 hours (d) 20 hours

    9. A boat takes 4 hours for travelling downstream from point A to point B and coming back topoint A upstream. If the velocity of the stream is 2 kmph and the speed of the boat in still wateris 4 kmph, what is the distance between A and B ?(a) 4 kms (b) 6 km (c) 8 km (d) 9 km

    10. If a man rows at 6 kmph in still water and 4.5 kmph against the current, then his rate alongthe current is(a) 9.5 km/hr (b) 7.5 km/hr (c) 7 km/hr (d) 5.25 km/hr

    11. If a man's rate with the current is 11 kmph and the rate of the current is 1.5 kmph, then theman's rate against the current is :

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 41

    (a) 8 km/hr (b) 9.5 km/hr (c) 9 km/hr (d) 6.25 km/hr

    12. Speed of a hoat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. manrows to a place at a distance of 10.5 km and comes back to the starting point. The total timetaken by him is :(a) 16 hours (b) 18 hours (c) 20 hours (d) 24 hours

    13. A boat moves upstream at the rate of 1 km in 10 minutes and downstream at the rate of 1 kmin 6 minutes. The speed of the current is :(a) 1 km/hr (b) 1.5 km/hr (c) 2 km/hr (d) 2.5 km/hr

    14. River is running at 2 kmph. If takes a man twice as long to row up as to row down the river.The rate of the man in still water is :(a) 6 km/hr (b) 4 km/hr (c) 10 km/hr (d) 8 km/hr

    15. A man rows to a place 48 km distant and back in 14 hours. He finds that he can row 4 kmwith the stream in the same time as 3 km against the stream. The rate of the stream is :(a) 1 km/hr (b) 1.8 km/hr (c) 3.5 km/hr (d) 1.5 km/hr

    16. The current of stream runs at 1 kmph. A motor boat goes 35 km upstream and back again tothe starting point in 12 hours. The speed of the motor boat in still water is :(a) 6 km/hr (b) 7 km/hr (c) 8 km/hr (d) 8.5 km/hr

    17. A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 kmupstream and 24 km downstream in 6 hours. The velocity of the current is :(a) 1 km/hr (b) 1.5 km/hr (c) 2 km/hr (d) 2.5 km/hr

    18. A man can row three-quarters of a kilometer against the stream in 11 minutes and returnsin 7 minutes. The speed of the man is still water is :(a) 2 km/hr (b) 3 km/hr (c) 4 km/hr (d) 5 km/hr

    19. The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distancetravelled downstream in 12 minutes is :(a) 3.6 km (b) 2.4 km (c) 1.2 km (d) 1.8 km

    20. A man can row 5 kmph in still water. If the river is running at 1kmph, it takes him 75minutes to row to a place and back. How far is the place?(a) 3 km (b) 2.5 km (c) 4.km (d) 5 km .

    21. If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph,then the man's rate along the current is :(a) 4.25 kmph (b) 6 kmph (c) 6.5 kmph (d) 8.5 kmph

    ANSWERS

  • REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS

    SITAMS 42

    1.(a) 2.(b) 3.(a) 4.(c) 5.(a) 6.(c) 7.(c) 8.(b) 9.(b) 10.(b)11.(a) 12.(a) 13.(c) 14.(a) 15.(a) 16.(a) 17.(c) 18.(d) 19.(a) 20.(a) 21.(c)

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