SPEED TIME AND DISTANCE Question Sheet (RACES)

Table Of Content

Practice Question

Answer Key

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SPEED TIME AND DISTANCE Question

Q.1 In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. If A has a start of 140 m, then A wins by:

a.60 m

b.40 m

c.20 m

d.10 m

Q.2 In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:

a.20 m

b.22.75 m

c.25 m

d.None of these

Q.3 In a one km race, A beats B by 36 m or 9 sec. Find A’s time to complete the race.

a.9 seconds

b.240 seconds

c.241 seconds

d.250 seconds

Q.4 A can run 440 m in 42s and B in 44s. By how many seconds will B win If he had 30 meters start?

a.1 second

b.2 second

c.3 second

d.4 second

Q.5 In a 1500m race, A beats B by 150m and in the same race B beats C by 75m. By what distance does A beats C?

a.200 m

b.215 m

c.217.5 m

d.222.5 m

Q.6 In a 10 km race. A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C?

a.1500 m

b.1600 m

c.1800 m

d.1900 m

Q.7 In a circular race of 2400m, A and B start from the same point and at the same time with speeds of 27km/hr. and 45 km/hr. Find when will they meet again for the first time on the track when they are running in the Opposite direction?

a.120 seconds

b.150 seconds

c.180 seconds

d.240 seconds

Q.8 A, B and C run around a circular track of length 1200 m with respective speeds 9, 18, 27 kmph. If they started at the same time from the same point and run in the same direction when will they meet for the first time?

a.360 sec

b.480 sec 

c.240 sec

d.None of these

Q.9 Two friends A and B simultaneously start running around a circular track. They run in the same direction. A travels at 6 m/s and B runs at b m/s. If they cross each other at exactly two points on the circular track and b is a natural number less than 30, how many values can b take?

a.3

b.4

c.5

d.7

Q.10 A and B are running in the same direction starting from a point P on a circular track of the length 1200 meter with speeds of 30 m/sec and 50 m/sec respectively. At what time they will meet for the first time anywhere on the track?

a.120 sec

b.30 sec

c.60 sec

d.50 sec

Q.11 A and B walk around a circular path of 900 metre in circumference, starting together from the same point in the same direction. If their speeds are 150 metre per minute and 200 metre per minute respectively, after how many minutes will they be again at the starting point?

a.9 minutes

b.12 minutes

c.15 minutes

d.18 minutes

Q.12 A can run one full round of a circular track in 6 min and B in 15 min.  If both A and B start simultaneously from the same starting point then How many times would they met in the time B has completed 10 rounds when running in same direction?

a.10 times

b.15 times

c.20 times

d.25 times

Q.13 A can run one full round of a circular track in 6 min and B in 15 min.  If both A and B start simultaneously from the same starting point then How many times would they met in the time B has completed 10 rounds when running in opposite direction?

a.20 times

b.25 times

c.30 times

d.35 times

Q.14 In a 100m race, A beats B by 20m or 5 seconds. If B beats C by 20m in the same race, by what distance will A beat C in a 250m race?

a.40 m

b.80 m

c.60 m

d.90 m

Q.15 Two circular tracks T1 and T2 of radii 100 m and 20 m, respectively touch at a point A. Starting from A at the same time, Ram and Rahim are walking on track T1 and track T2 at speeds 15 km/hr and 5 km/hr respectively. The number of full rounds that Ram will make before he meets Rahim again for the first time is

a.2

b.3

c.4

d.5

Q.16 Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

a.4.2

b.4.6

c.4.8

d.5.2

Q.17 In a 1km race, A beats B by 60 seconds and B beats C by 45 seconds. By how much time will A beat C in a 500m race?

a.105 sec

b.52.5 sec

c.60 sec

d.80 sec

Q.18 John jogs on track A at 6 km/h and Mary jogs on track B at 7.5 km/h. The total length of tracks A and B is 325 metres. While John makes 9 rounds of track A, Mary makes 5 rounds of track B. In how many seconds will Mary make one round of track A?

a.49

b.48

c.47

d.45

Q.19 Two ants A and B start from a point P on a circle at the same time, with A moving clock-wise and B moving anti-clockwise. They meet for the first time at 10:00 am when A has covered 60% of the track. If A returns to P at 10:12 am, then B returns to P at

a.10 : 18 am

b.10 : 25 am

c.10 : 27 am

d.10 : 45 am

Q.20 Three friends A, B and C decide to run around a circular track. They start at the same time and run in the same direction. A is the quickest and when A finishes a lap, it is seen that C is as much behind B as B is behind A. When A completes 3 laps, C is the exact same position on the circular track as B was when A finished 1 lap. Find the ratio of the speeds of A, B and C?

a.3 : 2 : 1

b.4 : 3 : 2

c.5 : 3 : 1

d.5 : 4 : 2

Q.21 In a race of three horses, the first beat the second by 11 metres and the third by 90 metres. If the second beat the third by 80 metres, what was the length of the race (in meters)?Q.22 Rakesh and Brijesh start running simultaneously from point A and point B respectively, on a circular track of length 150 meters at a speed of 5 m/s and 3 m/s in the same direction from diametrically opposite ends. When will they meet at the point B from where Brijesh starts running?

a.15 seconds

b.30 seconds

c.50 seconds

d.They will never meet at point B

Q.23 In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

Q.24 Shyam and Shreya start running simultaneously from a point O on a circular track in same direction. If the ratio of their speeds is 7 : 4 respectively, then how many times do they meet each other till they reach O again?

a.2

b.3

c.4

d.7

Q.25 In a 1000m Bike race, Bike A beats Bike B by 200m.In a 500m race, Bike B beats Bike C by 50m.In a 3600m race, If Bike A beats C by 56 seconds. How long would bike B take to travel a distance of 3000m?

a.100 seconds

b.120 seconds

c.150 seconds

d.200 seconds

Q.26 Arun and Barun start running simultaneously from same point on a circular track in opposite directions and with speeds in the ratio of 3 : 5 respectively. Every time they meet, they interchange their speeds and also reverse their directions. At how many distinct points on the track do they meet each other, if they run continuously?

a.2

b.3

c.5

d.8

Q.27 In a race, Dipesh beats Himanshu by 120 metres, Himanshu beats Hardik by 150 metres and Dipesh beats Hardik by 240 metres. If they all run a 2000 metres race, then find what distance will be covered by Hardik (in metres) in the time Dipesh covers 1350 metres.Q.28 A, B, C, and D are moving on a circular track in the same direction. All started running simultaneously and from the same point such that the ratio of their speeds is 1 : 2 : 3 : 4. At how many distinct points any two of them will meet.

a.1

b.2

c.3

d.4

Q.29 A swimming pool is of length 50 m. A and B enter a 300 m race starting simultaneously at one end of the pool at speeds of 3 m/s and 5 m/s. How many times will they meet while before B completes the race?

a.Once

b.Twice

c.Thrice

d.4-Times

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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.