Quantitative Aptitude

Races and Games: Practice Questions with Answers

14 practice questions on Races and Games, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   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.

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   Answer: 7.5 m/s

   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.

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2. Q.2

   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?

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   Answer: 20 m

   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.

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3. Q.3

   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?

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   Answer: 6 seconds

   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.

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4. Q.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)?

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   Answer: 40 m

   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.

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5. Q.5

   A and B run a 400 m race. A wins by 40 m or 10 seconds. Find A's speed.

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   Answer: 40/9 m/s ≈ 4.44 m/s

   Solution:

   1. The "40 m or 10 seconds" phrasing means: the 40 m that B was still short of finishing is exactly what B would have covered in the 10 extra seconds. So B's speed = 40/10 = 4 m/s.
   2. B's time to finish the full 400 m = 400/4 = 100 seconds.
   3. A finishes 10 seconds before that: A's time = 100 − 10 = 90 seconds.
   4. A's speed = 400/90 = 40/9 ≈ 4.44 m/s.

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6. Q.6

   In a race, A can give B a start of 10 m in a 100 m race, and B can give C a start of 10 m in the same 100 m race. If A, B and C all ran a 100 m race together, by how much would A beat C?

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   Answer: 19 m

   Solution:

   1. A gives B a 10 m start in 100 m, so while A covers 100 m, B covers 90 m: speed ratio B/A = 90/100 = 9/10.
   2. Similarly, speed ratio C/B = 9/10.
   3. Combine the ratios (don't just add the distances): speed ratio C/A = (9/10) × (9/10) = 81/100.
   4. So while A covers 100 m, C covers 81 m. A beats C by 100 − 81 = 19 m (not 10 + 10 = 20 m).

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7. Q.7

   In a 100 m race, A gives B a start of 5 seconds. If B's speed is 4 m/s, what is this equivalent to as a distance start?

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   Answer: 20 m

   Solution:

   1. A time start of T seconds is equivalent to that runner covering T × speed metres before the other even begins.
   2. Equivalent distance = 5 × 4 = 20 m.

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8. Q.8

   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?

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   Answer: 2 seconds

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9. Q.9

   In a race, A can give B a start of 20 m in a 100 m race, and B can give C a start of 10 m in the same 100 m race. By how much would A beat C in a 100 m race among all three?

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   Answer: 28 m. Speed ratio C/A = (80/100) × (90/100) = 18/25; C covers 72 m while A covers 100 m.

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10. Q.10

    In a 200 m race, A gives B a start of 8 seconds. If B's speed is 5 m/s, what is this equivalent to as a distance start?

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    Answer: 40 m. 8 × 5.

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11. Q.11

    In a 250 m race, A's speed is 10 m/s and B's speed is 8 m/s. What start should A give B for a dead heat?

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    Answer: 50 m. A's time = 25 s; B covers 200 m in 25 s; start = 250 − 200.

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12. Q.12

    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?

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    Answer: 40 m

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13. Q.13

    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?

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    Answer: 75 m

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14. Q.14

    A and B run a 500 m race. A wins by 50 m or 10 seconds. Find A's speed.

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    Answer: 50/9 m/s ≈ 5.56 m/s. B's speed = 50/10 = 5 m/s; B's time = 100 s; A's time = 90 s; A's speed = 500/90.

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