Problems on Trains, Boats and Streams

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<p>REASONING AND QUANTITATIVE APTITUDE</p> <p>PROBLEMS ON TRAINS, BOATS AND STREAMS</p> <p>Module Name: PROBLEMS ON TRAINS,BOATSAND STREAMS.SITAMS 1</p> <p>REASONING AND QUANTITATIVE APTITUDE</p> <p>PROBLEMS ON TRAINS, BOATS AND STREAMS</p> <p>MODULE OBJECTIVE: Decision making for planning, policy and management relies increasingly on the quantitative reasoning, which entails the collection, analysis and interpretation of quantitative data. This course is designed to introduce principles and techniques to solve trains, boats and streams related problems. Develop logical reasoning in a problem solving framework. One goal is to develop a disciplined logical analysis of word problems. Such reasoning is the foundation for buildings simple mathematical models of problems-models implicit on trains, boats and streams. However a logical mind will serve a person well in any field.</p> <p>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</p> <p>SITAMS</p> <p>2</p> <p>REASONING AND QUANTITATIVE APTITUDE</p> <p>PROBLEMS ON TRAINS, BOATS AND STREAMS</p> <p>PREREQUISITES: 1. a km/hr= (a* 5/18) m/s.</p> <p>2. a m / s = (a*18/5) km/hr.</p> <p>3 Time taken by a train of length 1 metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover 1 metres.</p> <p>4. Time taken by a train of length 1 metres to pass a stationary object of length b metres is the time taken by the train to cover (1 + b) metres.</p> <p>5. Suppose two trains or two bodies are moving in the same direction at u m / s and v m/s, where u &gt; v, then their relatives speed = (u - v) m / s.</p> <p>6. Suppose two trains or two bodies are moving in opposite directions at u m / s and v m/s, then their relative speed is = (u + v) m/s.</p> <p>7. If two trains of length a metres and b metres are moving in opposite directions at u m / s and v m/s, then time taken by the trains to cross each other = (a + b)/(u+v) sec.</p> <p>8.If two trains of length a metres and b metres are moving in the same directionat u m / s and v m / s, then the time taken by the faster train to cross the slower train = (a+b)/(u-v) sec.</p> <p>9. If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then (A's speet) : (Bs speed) = (b1/2: a1/2).</p> <p>SITAMS</p> <p>3</p> <p>REASONING AND QUANTITATIVE APTITUDE</p> <p>PROBLEMS ON TRAINS, BOATS AND STREAMS</p> <p>SOLVED EXAMPLES: Ex.I. A train 100 m long is running at the speed of 30 km / hr. Find the time taken by it 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, how long 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 a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed? (SASKEN 2003)</p> <p>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 sec x/8=(x+180)/20 20x = 8 (x + 180) x = 120.</p> <p>Length of the train = 120 m. Speed of the train = (120/8) m / sec = m / sec = (15 *18/5) kmph = 54 km Ex. 4. A train 150 m long is running with a speed of 68 kmph. In what time will it pass a man 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/secSITAMS 4</p> <p>REASONING AND QUANTITATIVE APTITUDE</p> <p>PROBLEMS ON TRAINS, BOATS AND STREAMS</p> <p>Time taken by the train to cross the man</p> <p>I</p> <p>= 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 train is 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 sec Ex. 6. Two trains 137 metres and 163 metres in length are running towards each other on parallel lines, one at the rate of 42 kmph and another at 48 kmpb. In what time will they be 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 sec Ex. 7. Two trains 100 metres and 120 metres long are running in the same direction with speeds of 72 km/hr,In howmuch time will the first train cross the second? (TCS 2007)</p> <p>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 the direction opposite to that of the train. Find the speed of the train.? Sol:Let the speed of the train be x kmph.SITAMS</p> <p>Speed of the train relative to man = (x + 5) kmph = (x + 5) *5/18 m/sec.</p> <p>5</p> <p>REASONING AND QUANTITATIVE APTITUDE</p> <p>PROBLEMS ON TRAINS, BOATS AND STREAMS</p> <p>Therefore 100/((x+5)*5/18)=6 30 (x + 5) = 1800 x = 55 Speed of the train is 55 kmph.</p> <p>Ex. 9. A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes.12 sec to pass a man walking at 6 kmph in the same direction in which the train is going . Find the length 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 an electric 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 platform 260 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.</p> <p>SITAMS</p> <p>6</p> <p>REASONING AND QUANTITATIVE APTITUDE</p> <p>PROBLEMS ON TRAINS, BOATS AND STREAMS</p> <p>Ex. 13. A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its 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 a man 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 a man 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.</p> <p>SITAMS</p> <p>7</p> <p>REASONING AND QUANTITATIVE APTITUDE</p> <p>PROBLEMS ON TRAINS, BOATS AND STREAMS</p> <p>EXERCISE PROBLEMS: 1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? (CSC 2008) A. 120 metres C. 324 metres Answer &amp; Explanation Answer: Option D Explanation: 5 Speed= 60 x = 18 m/sec B. 180 metres D. 150 metres</p> <p>50 3 m/sec. 50 x9 3 m = 150 m.</p> <p>Length of the train = (Speed x Time) =</p> <p>2. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: A. 45 km/hr C. 54 km/hr Answer &amp; Explanation Answer: Option B Explanation: Speed of the train relative to man = = 125 10 m/sec B. 50 km/hr D. 55 km/hr</p> <p>25 2 m/sec. 25 18 = x 2 5 km/hr = 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 can cross in 30 seconds, is:(CTS 2009) A. 200 mSITAMS</p> <p>B. 225 m8</p> <p>REASONING AND QUANTITATIVE APTITUDE</p> <p>PROBLEMS ON TRAINS, BOATS AND STREAMS</p> <p>C. 245 m Answer &amp; Explanation Answer: Option C Explanation: 5 25 Speed = 45 x = 18 m/sec 2 m/sec. Time = 30 sec. Let the length of bridge be x metres. 130 + x 25 Then, = 30 2 2(130 + x) = 750 x = 245 m.</p> <p>D. 250 m</p> <p>4. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is.(IBM 2008) A. 1 : 3 C. 3 : 4 B. 3 : 2 D. None of these</p> <p>Answer &amp; Explanation Answer: Option B Explanation: 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+ y 27x + 17y = 23x + 23y 4x = 6y x 3 = . y 2 5. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? A. 120 m C. 300 m Answer &amp; Explanation Answer: Option B Explanation: 5 Speed = 54 x 18 m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m.SITAMS 9</p> <p>B. 240 m D. None of these</p> <p>REASONING AND QUANTITATIVE APTITUDE</p> <p>PROBLEMS ON TRAINS, BOATS AND STREAMS</p> <p>Let the length of the platform be x metres. x + 300 Then, = 15 36 x + 300 = 540 x = 240 m.</p> <p>6. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?(TCS 2006) A. 65 sec C. 100 sec Answer &amp; Explanation Answer: Option B Explanation: 240 Speed = 24 m/sec = 10 m/sec. Required time = 240 + 650 sec = 89 sec. B. 89 sec D. 150 sec</p> <p>7. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is: A. 50 m C. 80 m Answer &amp; Explanation Answer: Option A Explanation: Let the length of each train be x metres. Then, distance covered = 2x metres. Relative speed = (46 - 36) km/hr 5 = 10 x 18 m/sec 25 = 9 m/sec 2x 25 = 36 9 2x = 100 x = 50. 8. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?(IGATE 2009)SITAMS 10</p> <p>B. 72 m D. 82 m</p> <p>REASONING AND QUANTITATIVE APTITUDE</p> <p>PROBLEMS ON TRAINS, BOATS AND STREAMS</p> <p>A. 40 sec C. 45 sec Answer &amp; Explanation Answer: Option A Explanation:</p> <p>B. 42 sec D. 48 sec</p> <p>Formula for converting from km/hr to m/s: X km/hr = 5 25 = m/sec. 18 m/sec 2 Total distance to be covered = (360 + 140) m = 500 m. Distance Formula for finding Time = Speed 500 x 2 Required time = = 40 sec. 25 sec Therefore, Speed = 45 x</p> <p>Xx</p> <p>5 m/s. 18</p> <p>9. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:(PATNI 2008) A. 36 C. 48 B. 45 D. 49</p> <p>Answer &amp; Explanation Answer: Option C Explanation: Relative speed = (60+ 90) km/hr 5 = 150 x 18 m/sec 125 = 3 m/sec. Distance covered = (1.10 + 0.9) km = 2 km = 2000 m. 3 Required time = 2000 x 125 sec = 48 sec. 10. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger? A. 3.6 sec C. 36 sec Answer &amp; Explanation Answer: Option C Explanation:SITAMS 11</p> <p>B. 18 sec D. 72 sec</p> <p>REASONING AND QUANTITATIVE APTITUDE</p> <p>PROBLEMS ON TRAINS, BOATS AND STREAMS</p> <p>Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr. 5 = 36 x 18 m/sec = 10 m/sec. Distance to be covered = (240 + 120) m = 360 m. 360 Time taken = = 36 sec. 10 sec</p> <p>11. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?(HCL 2009) A. 230 m C. 260 m E. None of these Answer &amp; Explanation Answer: Option A Explanation: Relative speed = (120 + 80) km/hr 5 = 200 x 18 m/sec 500 = 9 m/sec. Let the length of the other train be x metres. x + 270 500 Then, = 9 9 x + 270 = 500 x = 230. 12. A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?(CTS 2005) A. 230 m C. 260 m Answer &amp; Explanation Answer: Option D Explanation: 5 Speed = 72 x = 20 m/sec. 18 m/sec Time = 26 sec. Let the length of the train be x metres. Then, x + 250 = 20SITAMS 12</p> <p>B. 240 m D. 320 m</p> <p>B. 240 m D. 270 m</p> <p>REASONING AND QUANTITATIVE APTITUDE</p> <p>PROBLEMS ON TRAINS, BOATS AND STREAMS</p> <p>26 x + 250 = 520 x = 270. 13. Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is: (CAT 2010) A. 30...</p>