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Races and Games Questions with Solutions

A race is just Time-Speed-Distance with a finish line — the twist is "start" (a head start in distance or time) and "beats by" (the gap at the finish), both of which just mean comparing how far each runner has gone at a shared moment in time. Here’s the concept, four fully worked examples covering each standard pattern, and a few to try yourself.

The concept, quickly

  • "A beats B by X metres" means: at the moment A finishes, B still has X metres left to run.
  • "A gives B a start of X metres" means B only has to cover (total distance − X) to finish — B effectively starts X metres ahead.
  • "A gives B a start of X seconds" means B starts running X seconds before A does — add X seconds to A’s finishing time to get B’s head-start-adjusted clock.
  • For a "dead heat" (both finish together), set up the condition that both cover their required distance in exactly the same time, then solve for the unknown.

Worked examples

1. A and B run a 100 m race. A finishes in 10 seconds, and B finishes in 12.5 seconds (both at constant speed). By what distance does A beat B?

Solution

  1. B’s speed = 100 / 12.5 = 8 m/s.
  2. At t = 10 seconds (when A finishes), B has covered 8 × 10 = 80 m.
  3. A beats B by 100 − 80 = 20 m.

Answer: 20 m

2. In a 100 m race, A gives B a start of 20 m. A’s speed is 10 m/s and B’s speed is 5 m/s. By how much time does A beat B?

Solution

  1. A runs the full 100 m: time = 100 / 10 = 10 seconds.
  2. B only needs to cover 100 − 20 = 80 m: time = 80 / 5 = 16 seconds.
  3. A beats B by 16 − 10 = 6 seconds.

Answer: 6 seconds

3. In a 200 m race, A gives B a start of 4 seconds and still beats him by 20 m. If A’s speed is 10 m/s, find B’s speed.

Solution

  1. A’s time for 200 m = 200 / 10 = 20 seconds.
  2. B started 4 seconds earlier, so B has been running for 20 + 4 = 24 seconds when A finishes.
  3. A beats B by 20 m, so in those 24 seconds B covered 200 − 20 = 180 m.
  4. B’s speed = 180 / 24 = 7.5 m/s.

Answer: 7.5 m/s

4. In a 200 m race, A’s speed is 10 m/s and B’s speed is 8 m/s. What start should A give B so that the race ends in a dead heat (both finish together)?

Solution

  1. A’s time to finish 200 m = 200 / 10 = 20 seconds.
  2. In that same 20 seconds, B covers 8 × 20 = 160 m.
  3. For a dead heat, B’s required distance must also be 160 m, so the start = 200 − 160 = 40 m.

Answer: 40 m

Try these yourself

Identify which pattern applies, then check against the answer.

1. A and B run a 200 m race. A finishes in 20 seconds, and B finishes in 25 seconds (both at constant speed). By what distance does A beat B?

Answer: 40 m

2. In a 150 m race, A gives B a start of 30 m. A’s speed is 15 m/s and B’s speed is 10 m/s. By how much time does A beat B?

Answer: 2 seconds

3. In a 300 m race, A’s speed is 12 m/s and B’s speed is 9 m/s. What start should A give B so that the race ends in a dead heat?

Answer: 75 m

Where this comes up

Races and Games is a dedicated sub-topic within the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk.

Practice more Races and Games questions

This page covers the concept and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Races and Games (and every other Quant/Reasoning/English topic) with instant scoring and explanations — free, no account required.

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