Quiz: Races and Games
This quiz follows Lesson 9: Problems on Races and Games from the course Time, Speed & Distance: Core Concepts for Competitive Exams. It tests your understanding of race terminology and the standard techniques used to solve race problems.
What you will practise
- Meaning of “beats by”: interpreting a win margin in distance or in time.
- Head start: how a start advantage in metres or seconds changes the effective race.
- Dead heat: recognising a tie and what it implies about speeds.
- Speed ratio from race results: converting race outcomes into ratios of speeds.
- Basic race problems: combining distances, times and margins correctly.
Work carefully with the distinction between a margin measured in distance and one measured in time, and remember that for a fixed distance, speed is inversely proportional to time. Good luck!
Q1. In a 100 m race, A beats B by 10 m. What distance had B covered when A finished the race?
When A finishes the full 100 m, B is 10 m behind, so B has covered ##100 - 10 = 90## m.
Q2. In a 200 m race, A beats B by 20 m. What is the ratio of the speed of A to the speed of B?
B covers ##200 - 20 = 180## m in the same time A covers 200 m. So the speed ratio is ##200:180 = 10:9##.
Q3. In a race, A beats B by 5 seconds. If A completes the race in 45 seconds, how long does B take?
A finishes in 45 s and is 5 s ahead of B, so B takes ##45 + 5 = 50## s.
Q4. A gives B a head start of 20 m in a 100 m race. This means that:
A head start of 20 m means B begins 20 m ahead of the starting line, so B has only 80 m left to run while A runs the full 100 m.
Q5. In a 100 m race, A gives B a start of 10 m and still beats him by 10 m. What distance does B run in total?
B starts 10 m ahead and is beaten by 10 m, so B covers ##100 - 10 - 10 = 80## m while A covers 100 m.
Q6. A race ends in a dead heat between A and B. What does this mean?
A dead heat means the competitors finish simultaneously, so neither beats the other.
Q7. In a 400 m race, A beats B by 40 m. If A's speed is 10 m/s, what is B's speed?
A takes ##400/10 = 40## s. In that time B covers ##400 - 40 = 360## m, so B's speed is ##360/40 = 9## m/s.
Q8. In a 100 m race, A beats B by 10 m and B beats C by 10 m. By how many metres does A beat C?
When A finishes 100 m, B has run 90 m. B beats C by 10 m over 100 m, so C runs ##90 \times \dfrac{90}{100} = 81## m. Thus A beats C by ##100 - 81 = 19## m.
Q9. A gives B a start of 4 seconds in a race and still wins by 2 seconds. If A takes 30 seconds to finish, how long does B take?
B starts 4 s early and loses by 2 s, so B's total time is ##30 + 4 + 2 = 36## s.
Q10. In a 1 km race, A beats B by 100 m. What is the ratio of A's speed to B's speed?
B covers ##1000 - 100 = 900## m in the time A covers 1000 m, so the ratio is ##1000:900 = 10:9##.
Q11. In a 100 m race, A beats B by 1 second. If B's speed is 5 m/s, how long does A take to finish?
B takes ##100/5 = 20## s. Since A beats B by 1 s, A takes ##20 - 1 = 19## s.
Q12. A can give B a start of 25 m in a 200 m race. What fraction of the race does B actually run?
B starts 25 m ahead, so B runs ##200 - 25 = 175## m out of 200 m, i.e. ##\dfrac{175}{200} = \dfrac{7}{8}##.
Q13. In a race, A beats B by 30 m or by 3 seconds. What is B's speed?
The 30 m margin is covered by B in 3 s, so B's speed is ##30/3 = 10## m/s.
Q14. In a 500 m race, A beats B by 50 m. If A's time is 50 seconds, what is B's speed?
B covers ##500 - 50 = 450## m in the same 50 s, so B's speed is ##450/50 = 9## m/s.
Q15. A gives B a head start of 20 m in a 100 m race, and the race ends in a dead heat. What is the ratio of A's speed to B's speed?
In the same time A runs 100 m while B runs ##100 - 20 = 80## m, so the ratio is ##100:80 = 5:4##.
Q16. In a 100 m race, A beats B by 20 m and B beats C by 20 m. By how many metres does A beat C?
When A finishes 100 m, B has run 80 m. B beats C by 20 m over 100 m, so C runs ##80 \times \dfrac{80}{100} = 64## m. Thus A beats C by ##100 - 64 = 36## m.
Q17. In a 200 m race, A beats B by 2 seconds. If A's speed is 10 m/s, what is B's speed?
A takes ##200/10 = 20## s, so B takes ##20 + 2 = 22## s. B's speed is ##200/22 = \dfrac{100}{11}## m/s.
Q18. A gives B a start of 10 m in a 100 m race and beats him by 10 m. What is the ratio of A's speed to B's speed?
A runs 100 m while B runs ##100 - 10 - 10 = 80## m, so the ratio is ##100:80 = 5:4##.
Q19. In a 100 m race, A beats B by 10 m. If A's time is 20 seconds, what is B's speed?
B covers ##100 - 10 = 90## m in the same 20 s, so B's speed is ##90/20 = 4.5## m/s.
Q20. In a 400 m race, A beats B by 20 m, and B beats C by 20 m. By how many metres does A beat C?
When A finishes 400 m, B has run 380 m. B beats C by 20 m over 400 m, so C runs ##380 \times \dfrac{380}{400} = 361## m. Thus A beats C by ##400 - 361 = 39## m.