Races and Games MCQs with Solutions

Races and games questions reduce to one idea: in the same time, runners cover distances in the ratio of their speeds. Below are 12 practice MCQs with fully worked solutions. Each solution has been checked step by step, so you can use these to learn the method as well as to test yourself.

Core concepts you need

• A beats B by x metres: when A finishes the race of length L, B has covered L − x metres in the same time.
• A beats B by t seconds: B takes t seconds longer than A to finish the race.
• A gives B a start of x metres: B only has to run L − x metres.
• Points in a game: "A can give B 20 points in a game of 100" means when A scores 100, B scores 80.

Practice questions

Q1. In a 100 m race, A finishes 10 m ahead of B. If A takes 10 seconds to finish, what is B's speed?

a) 10 m/s   b) 8 m/s   c) 9 m/s   d) 7 m/s

When A finishes 100 m in 10 s, B has covered 100 − 10 = 90 m in the same 10 s. B's speed = 90 ÷ 10 = 9 m/s. Answer: c) 9 m/s

Q2. In a 200 m race, A beats B by 20 m and B beats C by 20 m. By how many metres does A beat C?

a) 36 m   b) 38 m   c) 40 m   d) 42 m

When A runs 200 m, B runs 180 m. When B runs 200 m, C runs 180 m, so when B runs 180 m, C runs 180 × 180/200 = 162 m. So when A finishes 200 m, C has run 162 m, and A beats C by 200 − 162 = 38 m. Answer: b) 38 m

Q3. A runs 100 m in 12 seconds and B runs it in 15 seconds. By what distance does A beat B?

a) 10 m   b) 12 m   c) 15 m   d) 20 m

B's speed = 100 ÷ 15 = 20/3 m/s. In A's finishing time of 12 s, B covers (20/3) × 12 = 80 m. So A beats B by 100 − 80 = 20 m. Answer: d) 20 m

Q4. A runs 4 laps in the same time B runs 3 laps. If A takes 24 seconds per lap, how long does B take per lap?

a) 28 s   b) 30 s   c) 32 s   d) 36 s

In the common time T, A runs 4 laps, so T = 4 × 24 = 96 s. In the same 96 s, B runs 3 laps, so B takes 96 ÷ 3 = 32 s per lap. Answer: c) 32 s

Q5. A and B run a 5 km race. A beats B by 1,000 m. If A's speed is 15 km/h, find B's speed.

a) 12 km/h   b) 10 km/h   c) 9 km/h   d) 8 km/h

A's time = 5 ÷ 15 = 1/3 hour. In this time B covers 5 − 1 = 4 km. B's speed = 4 ÷ (1/3) = 12 km/h. Answer: a) 12 km/h

Q6. In a 900 m race, A runs at 9 m/s and beats B by 50 seconds. Find B's speed.

a) 5 m/s   b) 6 m/s   c) 7 m/s   d) 7.5 m/s

A's time = 900 ÷ 9 = 100 s. B takes 100 + 50 = 150 s for the same 900 m. B's speed = 900 ÷ 150 = 6 m/s. Answer: b) 6 m/s

Q7. A can give B a start of 40 m in a 400 m race and the race ends in a dead heat. What is the ratio of A's speed to B's speed?

a) 9 : 10   b) 10 : 9   c) 8 : 9   d) 9 : 8

They finish together, so in the same time A runs 400 m while B runs 400 − 40 = 360 m. Speed ratio = 400 : 360 = 10 : 9. Answer: b) 10 : 9

Q8. In a 200 m race, A beats B by 20 m or 5 seconds. How long does A take to finish the race?

a) 40 s   b) 45 s   c) 50 s   d) 55 s

"20 m or 5 seconds" means B covers the last 20 m in 5 s, so B's speed = 20 ÷ 5 = 4 m/s. B's time for 200 m = 200 ÷ 4 = 50 s. A finishes 5 s earlier, so A takes 50 − 5 = 45 s. Answer: b) 45 s

Q9. In a game of 100 points, A can give B 20 points and C 28 points. How many points can B give C in a game of 100?

a) 8   b) 10   c) 12   d) 15

When A scores 100, B scores 80 and C scores 72. So when B scores 100, C scores 72 × 100/80 = 90. B can give C 100 − 90 = 10 points. Answer: b) 10 points

Q10. In a 100 m race, A beats B by 10 m, and in a 100 m race B beats C by 10 m. By how much does A beat C in a 100 m race?

a) 18 m   b) 19 m   c) 20 m   d) 21 m

When A runs 100 m, B runs 90 m. When B runs 100 m, C runs 90 m, so when B runs 90 m, C runs 90 × 90/100 = 81 m. A beats C by 100 − 81 = 19 m. Answer: b) 19 m

Q11. In a 1,600 m race, A runs at 8 m/s and beats B by 200 seconds. Find B's speed.

a) 6 m/s   b) 4 m/s   c) 5 m/s   d) 7 m/s

A's time = 1600 ÷ 8 = 200 s. B takes 200 + 200 = 400 s for the full 1,600 m. B's speed = 1600 ÷ 400 = 4 m/s. Answer: b) 4 m/s

Q12. A runs 6 laps in the same time B runs 5 laps. If A takes 15 minutes per lap, how long does B take per lap?

a) 12 min   b) 14 min   c) 16 min   d) 18 min

In the common time T, A runs 6 laps, so T = 6 × 15 = 90 min. B runs 5 laps in the same 90 min, so B takes 90 ÷ 5 = 18 min per lap. Answer: d) 18 min

Quick recap

• Convert every "beats by distance" statement into distances covered in the same time, then compare as a ratio of speeds.
• Convert every "beats by time" statement into the loser's total time, then divide distance by time.
• For chained comparisons (A vs B, B vs C), multiply the ratios.

For timed practice on this and other arithmetic topics, try the sectional tests and full mocks on Pareeksha.