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- Question
In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
Options- A. 60 m
- B. 40 m
- C. 20 m
- D. 10 m
- Correct Answer
- 20 m
ExplanationTo reach the winning post A will have to cover a distance of (500 - 140)m, i.e., 360 m.While A covers 3 m, B covers 4 m.
While A covers 360 m, B covers ❨ 4 x 360 ❩m = 480 m. 3 Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.
∴ A wins by 20 m.
Races and Games problems
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- 1. In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:
Options- A. 21 m
- B. 26 m
- C. 28 m
- D. 29 m Discuss
Correct Answer: 28 m
Explanation:
A : B = 100 : 75B : C = 100 : 96.
∴ A : C = ❨ A x B ❩ = ❨ 100 x 100 ❩ = 100 = 100 : 72. B C 75 96 72 ∴ A beats C by (100 - 72) m = 28 m.
- 2. In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:
Options- A. 22.75 m
- B. 25 m
- C. 19.5 m
- D.
7 4 m 7
Discuss
Correct Answer: 25 m
Explanation:
A : B = 200 : 169.A : C = 200 : 182.
C = ❨ C x A ❩ = ❨ 182 x 200 ❩ = 182 : 169. B A B 200 169 When C covers 182 m, B covers 169 m.
When C covers 350 m, B covers ❨ 169 x 350 ❩m = 325 m. 182 Therefore, C beats B by (350 - 325) m = 25 m.
- 3. A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:
Options- A. 100 m
- B.
111 1 m 9 - C. 25 m
- D. 50 m Discuss
Correct Answer: 100 m
Explanation:
When B runs 25 m, A runs 45 m. 2 When B runs 1000 m, A runs ❨ 45 x 1 x 1000 ❩m = 900 m. 2 25 ∴ B beats A by 100 m.
- 4. In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:
Options- A. 18 m
- B. 20 m
- C. 27 m
- D. 9 m Discuss
Correct Answer: 20 m
Explanation:
A : B = 100 : 90.A : C = 100 : 72.
B : C = B x A = 90 x 100 = 90 . A C 100 72 72 When B runs 90 m, C runs 72 m.
When B runs 100 m, C runs ❨ 72 x 100 ❩m = 80 m. 90 ∴ B can give C 20 m.
- 5. In a 200 metres race A beats B by 35 m or 7 seconds. A's time over the course is:
Options- A. 40 sec
- B. 47 sec
- C. 33 sec
- D. None of these Discuss
Correct Answer: 33 sec
Explanation:
B runs 35 m in 7 sec.∴ B covers 200 m in ❨ 7 x 200 ❩ = 40 sec. 35 B's time over the course = 40 sec.
∴ A's time over the course (40 - 7) sec = 33 sec.
- 6. A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:
Options- A. 5.15 kmph
- B. 4.14 kmph
- C. 4.25 kmph
- D. 4.4 kmph Discuss
Correct Answer: 4.14 kmph
Explanation:
A's speed = ❨ 5 x 5 ❩m/sec = 25 m/sec. 18 18 Time taken by A to cover 100 m = ❨ 100 x 18 ❩sec = 72 sec. 25 ∴ Time taken by B to cover 92 m = (72 + 8) = 80 sec.
∴ B's speed = ❨ 92 x 18 ❩kmph = 4.14 kmph. 80 5 - 7. At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?
Options- A. 30 points
- B. 20 points
- C. 10 points
- D. 12 points Discuss
Correct Answer: 10 points
Explanation:
A : B = 60 : 45.A : C = 60 : 40.
∴ B = ❨ B x A ❩ = ❨ 45 x 60 ❩ = 45 = 90 = 90 : 80. C A C 60 40 40 80 ∴ B can give C 10 points in a game of 90.
- 8. In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:
Options- A. 5.4 m
- B. 4.5 m
- C. 5 m
- D. 6 m Discuss
Correct Answer: 6 m
Explanation:
A : B = 100 : 90.A : C = 100 : 87.
B = B x A = 90 x 100 = 30 . C A C 100 87 29 When B runs 30 m, C runs 29 m.
When B runs 180 m, C runs ❨ 29 x 180 ❩m = 174 m. 30 ∴ B beats C by (180 - 174) m = 6 m.
- 9. A runs 1⅔ times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?
Options- A. 200 m
- B. 300 m
- C. 270 m
- D. 160 m Discuss
Correct Answer: 200 m
Explanation:
Ratio of the speeds of A and B = 5 : 1 = 5 : 3. 3 Thus, in race of 5 m, A gains 2 m over B.
2 m are gained by A in a race of 5 m.
80 m will be gained by A in race of ❨ 5 x 80 ❩m = 200 m. 2 ∴ Winning post is 200 m away from the starting point.
- 10. In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:
Options- A. 8 points
- B. 10 points
- C. 14 points
- D. 40 points Discuss
Correct Answer: 10 points
Explanation:
A : B = 100 : 80.A : C = 100 : 72.
∴ B = ❨ B x A ❩ = ❨ 80 x 100 ❩ = 10 = 100 = 100 : 90. C A C 100 72 9 90 ∴ B can give C 10 points.
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