Races and Games problems
- 1. In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:
Options- A. 86 sec
- B. 80 sec
- C. 76 sec
- D. None of these Discuss
Correct Answer: 80 sec
Explanation:
| B runs | 45 | m in 6 sec. |
| 2 |
| ∴ B covers 300 m in | ❨ | 6 x | 2 | x 300 | ❩sec | = 80 sec. |
| 45 |
- 2. 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 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.
- 3. 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 : 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.
- 4. 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.
- 5. 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 : 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.
- 6. 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:
B : 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.
- 7. 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 Discuss
Correct Answer: 20 m
Explanation:
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.
- 8. 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 |
- 9. 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 : 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.
- 10. 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 : 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.
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