CAT Time, Speed & Distance Questions

Distance, speed and time are linked by a rate relationship. Relative motion, journeys with several stages and meeting problems require consistent units and a clear account of each interval.

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Key concepts

• Distance = speed × time
• Relative speed
• Average speed and multi-stage journeys

CAT time, speed & distance practice questions

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Common mistakes

• Taking the arithmetic mean of speeds for unequal travel times.
• Mixing kilometres per hour with metres per second.

Practical solving approaches

• Draw a timeline or distance diagram for meetings and overtaking.
• Compute average speed using total distance divided by total time.

Time, Speed & Distance FAQs

When do I add relative speeds?

Add speed magnitudes when objects move toward each other along the same line; subtract them for motion in the same direction.

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CAT Time, Speed & Distance Questions

Distance, speed and time are linked by a rate relationship. Relative motion, journeys with several stages and meeting problems require consistent units and a clear account of each interval.

16 free practice questions

Key concepts

• Distance = speed × time
• Relative speed
• Average speed and multi-stage journeys

CAT time, speed & distance practice questions

Question 1Multiple choiceMEDIUM

Question 1

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Prashant and Sushant start driving towards the sea from point A and at the same time with speeds 50 km/hr and 60 km/hr respectively. The perpendicular distance between the sea and point A is 300 km. Prashant drives on this perpendicular path and Sushant drives on a path which is at 30 ° from the path which Prashant takes. Both of them had decided that as soon as they reach the sea, they would start driving towards each other along the sea. But Sushant drives on his path only for 300 km and then starts driving on a path which is perpendicular to the sea. How much distance does Prashant travel before he meets Sushant?

Choose an answer

A.393 kmB.533 kmC.359 kmD.Cannot be determined

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Question 2Multiple choiceMEDIUM

Question 2

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Khushi and Arushi start simultaneously from point A towards point B, which is 30 km away. Khushi travels at a constant speed of 10 kmph to reach the destination. After travelling for 10 minutes, Arushi had to go back to point A and without wasting any time, she again started travelling towards B. Arushi reached point B thirty minutes after Khushi. What is Arushi\'s approximate speed, if she travels at a constant speed throughout?

Choose an answer

A.8.6 kmphB.7.4 kmphC.6.8 kmphD.9.4 kmph

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Question 3Multiple choiceMEDIUM

Question 3

Select the correct alternative from the given choices.

Answer the questions independently of each other.

A and B started from point X towards Y at 11 am with constant speeds and C is travelling from Y to X at 40 kmph. Sum of their speeds of A and B was 100 kmph. At 3 pm, A met C, after another hour, C met B. After this, A and B interchanged their speeds. At what time will B overtake A?

Choose an answer

A.8.30 pmB.9 pmC.8 pmD.None of these

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Question 4Type in the answerMEDIUM

Question 4

Type in your answer in the input box provided below the question.

Answer the questions independently of each other.

A covers one third of the journey in 3 hours. Half of remaining distance in 4 hours and half in 5 hours. If average speed of A for the enitre journey was 54 kmph, then find the total distance (in km)covered during the journey.

Your answer

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Question 5Multiple choiceMEDIUM

Question 5

How long did Anil walk?

Refer to the data below and answer the questions that follow.

Everyday, Anil\'s driver takes the car from Anil\'s home at certain time, reaches his office exactly at 5 p.m., picks up Anil and drives him home, travelling at a constant speed throughout. One day, Anil left his office at 3 p.m. and started walking on the usual route towards his home. His driver picked him on the way and drove him home. Anil noted that he reached home 40 minutes earlier than his usual time.

Choose an answer

A.20 minutesB.40 minutesC.100 minutesD.80 minutes

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Question 6Multiple choiceEASY

Question 6

What was the speed with which Anil walked?

Refer to the data below and answer the questions that follow.

Everyday, Anil\'s driver takes the car from Anil\'s home at certain time, reaches his office exactly at 5 p.m., picks up Anil and drives him home, travelling at a constant speed throughout. One day, Anil left his office at 3 p.m. and started walking on the usual route towards his home. His driver picked him on the way and drove him home. Anil noted that he reached home 40 minutes earlier than his usual time.

Choose an answer

A.2 km/hrB.3 km/hrC.5 km/hrD.Data insufficient

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Question 7Multiple choiceMEDIUM

Question 7

Select the correct alternative from the given choices.

Answer the questions independently of each other.

In a 4000 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

Choose an answer

A.20 minB.15 minC.10 minD.5 min

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Question 8Multiple choiceMEDIUM

Question 8

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Karan and Arjun run a 100-metre race, where Karan beats Arjun by 10 metres. To do a favour to Arjun Karan starts 10 metres behind the starting line in a second 100-metre race. They both run at their earlier speeds. Which of the following is true in connection with the secondrace?

 

Choose an answer

A.Karan and Arjun rach the finishing line simultaneously.B.Arjun beats Karan by 1 metre.C.Arjun beats Karan by 11 metres.D.Karan beats Arjun by 1 metre.

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Question 9Multiple choiceMEDIUM

Question 9

Select the correct alternative from the given choices.

Answer the questions independently of each other.

In a 1000 metres race, Manish gives Ravi a headstart of 40 metres and beats him by 19 seconds. If Manish gives Ravi a headstart of 30 seconds, then Ravi beats Manish by 40 metres. Find the ratio of Manish\'s speed to Ravi\'s speed.

Choose an answer

A.

B.

C.

D.

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Question 10Multiple choiceMEDIUM

Question 10

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known 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 at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to

Choose an answer

A.6:15 amB.6:30 am C.6:45 amD.7:00 amE.7:15 am

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Question 11Type in the answerMEDIUM

Question 11

Type in your answer in the input box provided below the question.

Answer the questions independently of each other.

A thief escapes from prison and runs with a speed of 40 m per minute. A police officer starts following the thief after 5 minutes with a speed of 50 m per minute. The officer has a dog that runs with a speed of 60 m per minute. The dog runs to the thief and comes back to the police to show him the direction. It keeps moving to and fro between them, till the police catches the thief. Find the distance travelled by the dog in the direction of the thief.

Your answer

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Question 12Multiple choiceMEDIUM

Question 12

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

Refer to the data below and answer the questions that follow.

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

Choose an answer

A.10 a.m.B.10:10 a.m.C.10:20 a.m.D.10:30 a.m.

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Question 13Multiple choiceMEDIUM

Question 13

At what time does Shyam overtake Ram?

Refer to the data below and answer the questions that follow.

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

Choose an answer

A.10:20 a.m.B.10:30 a.m.C.10:40 a.m.D.10:50 a.m.

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Question 14Multiple choiceMEDIUM

Question 14

Select the correct alternative from the given choices

Ramit and Amit travel with uniform speed from A to B and B to A respectively, via the same route. Ramit starts at
5:00 am while Amit starts four hours later. They meet, on the way, at 1:10 pm. At what me do they reach their
destinations, if both of them reach at the same time?

Choose an answer

A.7 pmB.8 pmC.6:30 pmD.7:30 pm

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Question 15Type in the answerEASY

Question 15

Enter your response (as an integer) using the virtual keyboard in the box provided.

Three trains leave a station at intervals of half an hour in the same direction. The third train after travelling for 1
hour, meets the second train but this was half an hour after it meets the first train. Calculate the speed of the
second train(in kmph) relative to the first, if the distance between these meeting points is 30 km.

Your answer

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Question 16Multiple choiceMEDIUM

Question 16

Select the correct alternative from the given choices

Two dogs start running around a 480 m circular track from the same point at the same me in opposite directions and with speeds
in the ratio 7 : 9. Which of the following can be the distance of the starting point from the point where they meet for the seventh
time?

Choose an answer

A.305 mB.30 mC.21 mD.210 m

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Common mistakes

• Taking the arithmetic mean of speeds for unequal travel times.
• Mixing kilometres per hour with metres per second.

Practical solving approaches

• Draw a timeline or distance diagram for meetings and overtaking.
• Compute average speed using total distance divided by total time.

Time, Speed & Distance FAQs

When do I add relative speeds?

Add speed magnitudes when objects move toward each other along the same line; subtract them for motion in the same direction.

More Arithmetic practice

• Averages →
• Mixtures & Alligation →
• Percentages →
• Profit, Loss & Discount →
• Ratio, Proportion, Variation & Partnership →
• Simple & Compound Interest →
• Time & Work →