SPEED TIME AND DISTANCE Question Sheet (RELATIVE MOTION)

Table Of Content

Practice Question

Answer Key

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SPEED TIME AND DISTANCE Question

Q.1 Truck X leaves the city at 10 AM and the speed is 40km/hr. After 3 hours another truck Y leaves the city in the same direction as truck X. In how much time will truck Y be 20 km ahead of truck X if the speed of truck Y is 60 km/hr?

a.6 hours

b.7 hours

c.8 hours

d.9 hours

Q.2 A ship leave on a long voyage. When it is 18 miles from the shore, a seaplane, whose speed is ten times that of the ship, is sent to deliver mail. How far from the shore does the seaplane catch up with the ship?

a.20 miles

b.22 miles

c.24 miles

d.25 miles

Q.3 A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at

a.10 : 45 am

b.11 : 00 am

c.11 : 20 am

d.11 : 45 am

Q.4 At 9 am, Ajay and Vijay started walking together at the same speed for Udaipur railway station in order to reach in time to catch a train there at 11 am. When they were exactly midway, Vijay realized that he forget his ticket. Therefore he immediately rushed back home in a horse-cart, while Ajay continued walking towards the railway station. Vijay collected his ticket from home and took the same cart to the railway station and reached the station just in time to catch the train. What is the ratio of speeds of the horse cart to the walking speed of Ajay?

a.1 : 3

b.2 : 1

c.4 : 1

d.3 : 1

Q.5 Shanti's school normally finishes at 4 pm. Her mom drives from home to pick her up, reaching the school exactly at 4 pm. One day, a half-holiday is announced and the school finishes for the day at 1 pm. Rather than sitting and waiting, Shanting decides to starts walking towards home. Her mother meets her along the way and as a result they they reach home an hour earlier then normal. What is the ratio of Shanti's walking speed to her mother's driving speed?

a.1 : 4

b.1 : 2

c.1 : 5

d.1 : 8

Q.6 Kittu leaves her school every day at 4:00 PM and her mother receives her and they go home together. One day school left an hour earlier and in place of waiting for her mother, Kittu started walking towards her home, she met her mother on the way and they reach home 20 minutes earlier than usual. If speed of car was 60 km/hr, find speed at which kittu was walking.

a.10 kmph

b.12 kmph

c.15 kmph

d.20 kmph

Q.7 A thief steals at a car at 2.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?

a.4.30 p.m.

b.4.45 p.m.

c.5 p.m.

d.5.15 p.m.

Q.8 Amit going to college by bike sees college bus 120 meter ahead of him. After 40 seconds, the college bus is 180 meter behind. If the speed of Amit’s bike is 35 km/h, what is the speed of the college bus?

a.5 km/h

b.6 km/h

c.8 km/h

d.12 km/h

Q.9 A train sets off at 3 p.m. at the speed of 70 kmph. Another train starts at 4:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet ?

a.10 : 10 pm

b.9 : 50 pm

c.11 : 30 pm

d.10 : 30 pm

Q.10 Vansh drives a car 20% faster than that of Yash. Both started at the same time from Muzaffarnagar but unfortunately Vansh's car broke down on the way due to this he wasted 2 hour. Find the speed of the Vansh if both of them reached Delhi at the same time and the distance between Muzaffarnagar and Delhi is 150 km.

a.15 km/h

b.18 km/h

c.20 km/h

d.24 km/h

Q.11 Arun, Barun and Kiranmala from the same place and travel in the same direction at speeds of 30, 40 and 60 km per hour respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala a start?

a.3

b.3.5

c.4

d.4.5

Q.12 On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour. If they both move towards east, then they meet in 7 hrs. The difference between their speeds, in km per hour, is

a.46

b.52

c.48

d.50

Q.13 Three cars leave A for B in equal time intervals. They reach B simultaneously and then leave for Point C which is 240 km away from B. The first car arrives at C an hour after the second car. The third car, having reached C, immediately turns back and heads towards B. The first and the third car meet a point that is 80 km away from C. What is the difference between the speed of the first and the third car?

a.20 km/h

b.40 km/h

c.60 km/h

d.80 km/h

Q.14 Points A and B are 150 km apart. Cars 1 and 2 travel from A to B, but car 2 starts from A when car 1 is already 20 km away from A. Each car travels at a speed of 100 kmph for the first 50 km, at 50 kmph for the next 50 km, and at 25 kmph for the last 50 km. The distance, in km, between car 2 and B when car 1 reaches B is

a.4

b.5

c.3

d.6

Q.15 Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets Car 1 at Q, and Car 2 at P. If each car is moving in uniform speed then the ratio of the speed of Car 2 to that of Car 1 is

a.1 : 2

b.1 : 4

c.2 : 7

d.2 : 9

Q.16 Two cars travel the same distance starting at 10:00 am and 11:00 am, respectively, on the same day. They reach their common destination at the same point of time. If the first car travelled for at least 6 hours, then the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is

a.10

b.20

c.25

d.35

Q.17 A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motorcycle leaves A and moves towards B. Forty-five such motorcycles reach B by 11 am. All motorcycles have the same speed. If the cyclist had doubled his speed, how many motorcycles would have reached B by the time the cyclist reached B?

a.15

b.20

c.22

d.23

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ANSWERS FOR SPEED TIME AND DISTANCE QUESTION (RELATIVE MOTION)

1	2	3	4	5	6	7	8	9	10
B	A	B	D	C	B	C	C	C	A
11	12	13	14	15	16	17
C	D	C	B	B	B	A

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Frequently Asked Questions — Speed, Time and Distance for CAT and IPMAT 2026

What is the fundamental formula for Speed, Time and Distance?

Speed = Distance / Time, or equivalently Distance = Speed x Time. Always ensure units are consistent. Convert km/h to m/s by multiplying by 5/18, and m/s to km/h by multiplying by 18/5.

How many Speed, Time and Distance questions appear in CAT?

CAT typically has 2-4 questions from TSD each year, covering relative speed, boats and streams, trains, and circular track problems. TSD is a high-frequency topic and appears in IPMAT as well.

What is relative speed and how is it used?

Relative speed is the speed of one object relative to another. Moving in same direction: relative speed = |v1 - v2|. Moving in opposite directions: relative speed = v1 + v2. This is used in train or boat meeting time and overtaking problems.

How do I solve boat and stream problems?

Downstream speed = Boat speed + Stream speed. Upstream speed = Boat speed - Stream speed. Boat speed in still water = (downstream + upstream)/2. Stream speed = (downstream - upstream)/2.

What is the concept of average speed and when does it differ from mean speed?

Average speed = Total Distance / Total Time. It is NOT the arithmetic mean of speeds unless equal times are spent at each speed. For two equal distances at speeds u and v: Average speed = 2uv/(u+v) which is the harmonic mean.

How do I solve circular track problems in TSD?

For two people starting from the same point on a circular track: Time to meet = Track length / |Speed difference| (same direction) or Track length / (Speed sum) (opposite directions). Extend this for multiple meetings.

What are the key shortcuts for train problems in CAT?

Time for a train to cross a stationary object of length L0 = (Train length + L0) / Train speed. Time for two trains of lengths L1 and L2 to cross each other = (L1+L2) / relative speed.

How should I prepare Speed, Time and Distance for IPMAT 2026?

IPMAT tests TSD at moderate-to-hard level. Focus on: (1) Unit conversions, (2) Relative speed, (3) Boats and streams, (4) Average speed traps, (5) Circular motion. Solve 3-4 mixed TSD problems daily for 2 weeks to build speed.

What is the concept of time taken to meet when two people start at different times?

If Person A starts t1 hours before Person B and they travel toward each other, they meet when distance covered by A + distance covered by B equals Total distance. Account for A's head start: A has already covered Speed_A x t1 before B starts.

How does TSD connect to Ratio and Proportion in CAT questions?

At constant speed: Distance is proportional to Time. At fixed distance: Speed is inversely proportional to Time. If speed increases by r%, time decreases by r/(100+r)%. These ratio relationships appear frequently in CAT.