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Races and Games — Questions and Answers

Races and Games is Time and Distance dressed in sporting language. "A beats B by 20 m" means that when A finishes the full distance, B is still 20 m short — that single translation converts every race question into a speed ratio. Game questions work the same way, with points replacing metres.

18 solved questionsArithmetic AptitudeFree · no signup

Races and Games— Concepts, Formulas & Shortcuts

  • "A beats B by x metres" ⇒ when A covers the full distance d, B has covered d − x. Speed ratio A : B = d : (d − x).
  • "A gives B a start of x metres" ⇒ B runs only d − x while A runs d.
  • "A gives B a start of t seconds" ⇒ B begins t seconds earlier; equate the times.
  • A dead heat means both finish together — their times are equal.
  • "A game of 100" means the first player to score 100 points wins.
  • "A can give B 20 points in a game of 100" ⇒ when A scores 100, B scores 80.

Races and Games Practice Questions with Answers

Attempt each question first, then open the explanation. All 18 questions below are free to read and require no signup.

  1. Q1.In a 100 m race, A beats B by 10 m. The ratio of their speeds is:

    Easy
    • A9 : 10
    • B10 : 9
    • C1 : 10
    • D10 : 1
    +Show Answer & Explanation

    Answer: B. 10 : 9

    Explanation: In equal time A covers 100 m and B covers 90 m, so the speed ratio is 100 : 90 = 10 : 9.

    Races and Games question 1 of 18

  2. Q2.In a 200 m race, A gives B a start of 20 m and still beats him by 10 m. The ratio of their speeds is:

    Difficult
    • A20 : 17
    • B10 : 9
    • C4 : 3
    • D5 : 4
    +Show Answer & Explanation

    Answer: A. 20 : 17

    Explanation: B runs from the 20 m mark, so his race is 180 m; when A finishes 200 m, B is 10 m short and has run 170 m. Speed ratio = 200 : 170 = 20 : 17.

    Races and Games question 2 of 18

  3. Q3.In race terminology, "a game of 100" means:

    Easy
    • AThe game lasts 100 minutes
    • BThe player scoring 100 points first wins
    • CThere are 100 players
    • DEach player gets 100 chances
    +Show Answer & Explanation

    Answer: B. The player scoring 100 points first wins

    Explanation: The number names the target score: the first competitor to reach it wins the game.

    Races and Games question 3 of 18

  4. Q4.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?

    Difficult
    • A8
    • B10
    • C12
    • D15
    +Show Answer & Explanation

    Answer: B. 10

    Explanation: A : B = 100 : 80 and A : C = 100 : 72, so B : C = 80 : 72 = 100 : 90 → B can give C 10 points.

    Races and Games question 4 of 18

  5. Q5.A runs 1¾ times as fast as B. If A gives B a start of 84 m, how far must the winning post be so that both reach it together?

    Difficult
    • A168 m
    • B180 m
    • C196 m
    • D210 m
    +Show Answer & Explanation

    Answer: C. 196 m

    Explanation: Speed ratio = 7 : 4. In equal time, d/(d − 84) = 7/4 → 4d = 7d − 588 → d = 196 m.

    Races and Games question 5 of 18

  6. Q6.In a 500 m race the speeds of A and B are in the ratio 3 : 4, and A has a start of 140 m. A wins by:

    Difficult
    • A10 m
    • B20 m
    • C30 m
    • D40 m
    +Show Answer & Explanation

    Answer: B. 20 m

    Explanation: A runs 360 m in 360/3 = 120 time units; in that time B covers 4 × 120 = 480 m of his 500 m, so A wins by 20 m.

    Races and Games question 6 of 18

  7. Q7.In a 200 m race, A beats B by 20 m. The ratio of their speeds is:

    Easy
    • A9 : 10
    • B10 : 9
    • C20 : 18
    • D1 : 10
    +Show Answer & Explanation

    Answer: B. 10 : 9

    Explanation: In equal time A covers 200 m and B covers 180 m → 200 : 180 = 10 : 9.

    Races and Games question 7 of 18

  8. Q8.In a 100 m race, A beats B by 4 seconds. If B takes 25 seconds, A's time is:

    Easy
    • A20 s
    • B21 s
    • C22 s
    • D24 s
    +Show Answer & Explanation

    Answer: B. 21 s

    Explanation: A finishes 4 seconds sooner: 25 − 4 = 21 seconds.

    Races and Games question 8 of 18

  9. Q9.In a game of 150 points, A gives B 30 points. When A scores 150, B scores:

    Easy
    • A100
    • B110
    • C120
    • D130
    +Show Answer & Explanation

    Answer: C. 120

    Explanation: Giving 30 points means B is 30 behind at the finish: 150 − 30 = 120.

    Races and Games question 9 of 18

  10. Q10.In a kilometre race, A beats B by 50 m. The ratio of their speeds is:

    Moderate
    • A19 : 20
    • B20 : 19
    • C1 : 20
    • D50 : 1000
    +Show Answer & Explanation

    Answer: B. 20 : 19

    Explanation: A runs 1,000 m while B runs 950 m → 1000 : 950 = 20 : 19.

    Races and Games question 10 of 18

  11. Q11.A can run 400 m in 50 seconds and B in 60 seconds. By what distance does A beat B?

    Difficult
    • A50 m
    • B60 m
    • C66 2/3 m
    • D80 m
    +Show Answer & Explanation

    Answer: C. 66 2/3 m

    Explanation: B's speed = 400/60 = 20/3 m/s. In A's 50 s, B covers 20/3 × 50 = 333⅓ m, so A wins by 400 − 333⅓ = 66⅔ m.

    Races and Games question 11 of 18

  12. Q12.In a 100 m race, A gives B a start of 10 m and still beats him by 5 m. When A finishes, B has run:

    Difficult
    • A80 m
    • B85 m
    • C90 m
    • D95 m
    +Show Answer & Explanation

    Answer: B. 85 m

    Explanation: B's race is 90 m, and he is 5 m short at the finish, so he has covered 85 m.

    Races and Games question 12 of 18

  13. Q13.In a 400 m race, A beats B by 40 m. The ratio of their speeds is:

    Moderate
    • A9 : 10
    • B10 : 9
    • C8 : 9
    • D9 : 8
    +Show Answer & Explanation

    Answer: B. 10 : 9

    Explanation: In equal time A covers 400 m and B covers 360 m → 400 : 360 = 10 : 9.

    Races and Games question 13 of 18

  14. Q14.In a game of 60 points, A gives B 12 points. When A scores 60, B scores:

    Easy
    • A40
    • B44
    • C48
    • D52
    +Show Answer & Explanation

    Answer: C. 48

    Explanation: B is 12 points behind at the finish: 60 − 12 = 48.

    Races and Games question 14 of 18

  15. Q15.In a 100 m race, A beats B by 5 seconds. If A takes 20 seconds, B's time is:

    Easy
    • A22 s
    • B23 s
    • C25 s
    • D30 s
    +Show Answer & Explanation

    Answer: C. 25 s

    Explanation: B takes 5 seconds longer: 20 + 5 = 25 seconds.

    Races and Games question 15 of 18

  16. Q16.In a 500 m race, A beats B by 50 m. The ratio of their speeds is:

    Moderate
    • A9 : 10
    • B10 : 9
    • C5 : 4
    • D4 : 5
    +Show Answer & Explanation

    Answer: B. 10 : 9

    Explanation: A covers 500 m while B covers 450 m → 500 : 450 = 10 : 9.

    Races and Games question 16 of 18

  17. Q17.A can run 200 m in 25 seconds. His speed is:

    Easy
    • A6 m/s
    • B8 m/s
    • C10 m/s
    • D12 m/s
    +Show Answer & Explanation

    Answer: B. 8 m/s

    Explanation: 200/25 = 8 m/s.

    Races and Games question 17 of 18

  18. Q18."A gives B a start of 30 m in a 300 m race" means B runs:

    Moderate
    • A270 m
    • B300 m
    • C330 m
    • D150 m
    +Show Answer & Explanation

    Answer: A. 270 m

    Explanation: B begins 30 m ahead, so his running distance is 300 − 30 = 270 m.

    Races and Games question 18 of 18

Races and Games — Frequently Asked Questions

What does "A beats B by 10 m in a 100 m race" tell me?+

When A has run the whole 100 m, B has run only 90 m in the same time. Since the times are equal, the speeds are in the ratio 100 : 90 = 10 : 9.

How do I combine two games results?+

Convert both to a common scale. If A : B = 100 : 80 and A : C = 100 : 72, then B : C = 80 : 72 = 100 : 90, so B can give C 10 points in a game of 100.

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