1.3 Marks

At his usual rowing rate, Rahul can travel 12 miles downstream in a certainriver in six hours less than it takes him to travel the same distanceupstream. But if he could double his usual rowing rate for this 24 milesround trip, the downstream 12 miles would then take only one hour lessthan the upstream 12 miles. What is the speed of the current in miles perhour?

[CAT 2001]

1)

2)

3)

4)

View Solution

2.3 Marks

Shyama and Vyom walk up an escalator (moving stairway). The escalatormoves at a constant speed. Shyama takes three steps for every two ofVyom's steps. Shyama gets to the top of the escalator after having taken25 steps. While Vyom (because his slower pace lets the escalator do alittle more of the work) takes only 20 steps to reach the top. If the escalatorwere turned off, how many steps would they have to take to walk up?

[CAT 2001]

1) 40

2) 50

3) 60

4) 80

View Solution

3.3 Marks

A train X departs from station A at 11.00 a.m. for station B, which is 180km away. Another train Y departs from station B at 11.00 a.m. for stationA. Train X travels at an average speed of 70 km/hr and does not stopanywhere until it arrives at station B. Train Y travels at an average speed

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Section I

of 50 km/hr, but has to stop for 15 minutes at station C, which is 60 kmaway from station B enroute to station A. Ignoring the lengths of the trains,what is the distance, to the nearest km, from station A to point where thetrains cross other?

[CAT 2001]

1) 112

2) 118

3) 120

4) None of these

View Solution

4.3 Marks

Three runners A, B and C run a race, with runner A finishing 12 metresahead of runner B and 18 metres ahead of runner C, while runner Bfinishes 8 metres ahead of runner C. Each runner travels the entiredistance at a constant speed. What was the length of the race?

[CAT 2001]

1) 36 metres

2) 48 metres

3) 60 metres

4) 72 metres

View Solution

Group Question

Answer the following questions based on the information given below.

Common Data

5.3 Marks

Manasa makes the 200 km trip from Mumbai to Pune at a steadyspeed of 60 km/hour. What is the amount of petrol consumed for thejourney?

1) 12.5 litres

2) 13.33 litres

3) 16 litres

4) 19.75 litres

View Solution

View Solution

6.3 Marks

Manasa would like to minimize the fuel consumption for the trip bydriving at the appropriate speed. How should she change thespeed?

1) Increase the speed

2) Decrease the speed

3) Maintain the speed at 60 km/hour

4) Cannot be determined

View Solution

7.3 Marks

Only a single rail track exists between station A and B on a railway line.One hour after the north bound superfast train N leaves station A forstation B, a south passenger train S reaches station A from station B. Thespeed of the superfast train is twice that of a normal express train E, whilethe speed of a passenger train S is half that of E. On a particular day Nleaves for station B from station A, 20 minutes behind the normalschedule. In order to maintain the schedule both N and S increased theirspeed. If the superfast train doubles its speed, what should be the ratio(approximately) of the speed of passenger train to that of the superfasttrain so that passenger train S reaches exactly at the scheduled time atthe station A on that day?

[CAT 2002]

1) 1 : 3

2) 1 : 4

3) 1 : 5

4) 1 : 6

View Solution

8.3 Marks

On a 20 km tunnel connecting two cities A and B there are three gutters.The distance between gutter 1 and 2 is half the distance between gutter 2and 3. The distance from city A to its nearest gutter, gutter 1 is equal to thedistance of city B from gutter 3. On a particular day the hospital in city Areceives information that an accident has happened at the third gutter. Thevictim can be saved only if an operation is started within 40 minutes. Anambulance started from city A at 30 km/hr and crossed the first gutter after5 minutes. If the driver had doubled the speed after that, what is themaximum amount of time the doctor would get to attend the patient at thehospital? Assume 1 minute is elapsed for taking the patient into and out ofthe ambulance.

[CAT 2002]

1) 4 minutes

2) 2.5 minutes

3) 1.5 minutes

4) Patient died before reaching the hospital

View Solution

9.3 Marks

There is a tunnel connecting city A and B. There is a CAT which isstanding at 3/8 the length of the tunnel from A. It listens a whistle of thetrain and starts running towards the entrance where, the train and the CATmeet. In another case, the CAT started running towards the exit and thetrain again met the CAT at the exit. What is the ratio of their speeds?

[CAT 2002]

1) 4 : 1

2) 1 : 2

3) 8 : 1

4) None of these

View Solution

10.3 Marks

In a 4000 meter race around a circular stadium having a circumference of1000 meters, the fastest runner and the slowest runner reach the samepoint at the end of the 5th minute, for the first time after the start of therace. All the runners have the same starting point and each runnermaintains a uniform speed throughout the race. If the fastest runner runs attwice the speed of the slowest runner, what is the time taken by the fastestrunner to finish the race?

[CAT 2003 Leaked Test]

1) 20 min

2) 15 min

3) 10 min

4) 5 min

View Solution

11.3 Marks

Karan and Arjun run a 100 metre race, where Karan beats Arjun by 10metres. To do a favour to Arjun, Karan starts 10 metres behind the startingline in a second 100 metre race. They both run at their earlier speeds.

line in a second 100 metre race. They both run at their earlier speeds.

Which of the following is true in connection with the second race?

[CAT 2004]

1) Karan and Arjun reach the finishing line simultaneously.

2) Arjun beats Karan by 1 metre.

3) Arjun beats Karan by 11 metres.

4) Karan beats Arjun by 1 metre.

View Solution

12.3 Marks

If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If hecycles at 15 km/hr, he will arrive at the same place at 11 a.m. At whatspeed must he cycle to get there at noon?

[CAT 2004]

1) 11 km/hr

2) 12 km/hr

3) 13 km/hr

4) 14 km/hr

View Solution

13.3 Marks

Two boats, travelling at 5 and 10 kms per hour, head directly towards eachother. They begin at a distance of 20 kms from each other. How far apartare they (in kms) one minute before they collide?

[CAT 2004]

1)

2)

3)

4)

View Solution

14.3 Marks

A sprinter starts running on a circular path of radius r metres. Her averagespeed (in metres/minute) is πr during the first 30 seconds, πr/2 during next

speed (in metres/minute) is πr during the first 30 seconds, πr/2 during next

one minute, πr/4 during next 2 minutes, πr/8 during next 4 minutes, and so

on. What is the ratio of the time taken for the nth round to that for theprevious round?

[CAT 2004]

1) 4

2) 8

3) 16

4) 32

View Solution

Group Question

Answer the following questions based on the information given below.

Common Data

15.3 Marks

At what time do Ram and Shyam first meet each other?

1) 10:00 a.m.

2) 10:10 a.m.

3) 10:20 a.m.

4) 10:30 a.m.

View Solution

16.3 Marks

At what time does Shyam overtake Ram?

1) 10:20 a.m.

2) 10:30 a.m.

3) 10:40 a.m.

4) 10:50 a.m..

View Solution

17.3 Marks

Arun, Barun and Kiranmala start from the same place and travel in thesame direction at speeds of 30 km/hr, 40 km/hr and 60 km/hr respectively.Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun atthe same instant, how many hours after Arun did Kiranmala start?

[CAT 2006]

1) 3

2) 3.5

3) 4

4) 4.5

5) 5

View Solution

Group Question

Answer the following questions based on the information given below.

Common Data

18.3 Marks

What is the time difference between A and B?

1) 1 hour and 30 minutes

2) 2 hours

3) 2 hours and 30 minutes

4) 1 hour

5) Cannot be determined

View Solution

19.3 Marks

What is the plane’s cruising speed in km per hour?

1) 700

2) 550

3) 600

4) 500

5) Cannot be determined

View Solution

20.3 Marks

Rahim plans to drive from city A to station C, at the speed of 70 km perhour, to catch a train arriving there from B. He must reach C at least 15minutes before the arrival of the train. The train leaves B, located 500 kmsouth of A, at 8:00 am and travels at a speed of 50 km per hour. It isknown that C is located between west and northwest of B, with BC at 60°to AB. Also, C is located between south and southwest of A with AC at30° to AB. The latest time by which Rahim must leave A and still catch the

train is closest to

[CAT 2008]

1) 6:15 am

2) 6:30 am

3) 6:45 am

4) 7:00 am

5) 7:15 am

View Solution

21.3 Marks

Two straight roads R1 and R2 diverge from a point A at an angle of 120°.

Ram starts walking from point A along R1 at a uniform speed of 3 km/hr.

Shyam starts walking at the same time from A along R2 at a uniform

speed of 2 km/hr. They continue walking for 4 hours along their respectiveroads and reach points B and C on R1 and R2, respectively. There is a

straight line path connecting B and C. Then Ram returns to point A afterwalking along the line segments BC and CA. Shyam also returns to A afterwalking along line segments CB and BA. Their speeds remainunchanged. The time interval (in hours) between Ram’s and Shyam’sreturn to the point A is:

[CAT 2003 Re-Test]

1)

2)

3)

4)

View Solution