Races and Games problems
- 1. 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.
- 2. 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 : 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.
- 3. In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
Options- A. 20 m
- B. 25 m
- C. 22.5 m
- D. 9 m Discuss
Correct Answer: 20 m
Explanation:
| Distance covered by B in 9 sec. = | ❨ | 100 | x 9 | ❩m | = 20 m. |
| 45 |
∴ A beats B by 20 metres.
- 4. Raman covers 1 km in 8 min while suman covers the same distance in 10 min. By what distance does Raman beat Suman?
Options- A. 150 m
- B. 65 m
- C. 190 m
- D. 200 m Discuss
Correct Answer: 200 m
Explanation:
Raman covers 1 km in 8 min
and suman cover 1 km in 10 min.
If they starts together, then distance covered by suman in 8 min
= (1000/10) x 8 = 800 m
? Raman will beat suman by (1000 - 800 ) m = 200 m
- 5. In a race of 150 m, A gives B a start of 20 m. What distance will be covered by B?
Options- A. 100 m
- B. 130 m
- C. 170 m
- D. 160 m Discuss
Correct Answer: 130 m
Explanation:
Required distance = (150 - 20) m = 130 m
- 6. In a race, P gives Q a start of 25 m making length of race for Q a distance of 175 m. Find the total length of race.?
Options- A. 250 m
- B. 200 m
- C. 225 m
- D. 235 m Discuss
Correct Answer: 200 m
Explanation:
Required length = (175 + 25)m = 200 m
- 7. In a 800 m race, A gives some start to B and this makes the length of race for B 725 m. What start does B get from A?
Options- A. 22 m
- B. 35 m
- C. 45 m
- D. 75 m Discuss
Correct Answer: 75 m
Explanation:
Start given by A to B = (800 - 725)m = 75 m
- 8. In a game of 100 points, A scores 100 points while B scores only 65 points. In this game, how much points can A give to B?
Options- A. 45
- B. 35
- C. 25
- D. 55 Discuss
Correct Answer: 35
Explanation:
Score of A = 100 points
Score of B = 65 points
? A can give (100 - 65 ) = 35 points to B.
- 9. In 1 km race, A beats B by 18 m or 9 s. Find the A' s time over the course.
Options- A. 391 s
- B. 591 s
- C. 491 s
- D. 500 s Discuss
Correct Answer: 491 s
Explanation:
Clearly, B covers 18 m in 9 s.
? B's time over the course = 9/18 x 1000 = 500 s
? A' s time over the course = (500 - 9) = 491 s
- 10. In a 1000 m race, X beats Y by 140 m or 14 s. What will be the X's time over the course?
Options- A. 86 s
- B. 90 s
- C. 95 s
- D. 76 s Discuss
Correct Answer: 86 s
Explanation:
Clearly, Y covers 140 m in 14 s
? Y' s time over the course = (14/140) x 1000 = 100 s
? X' s time over the course = 100 - 14 = 86 s
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