Races and Games problems
- 1. 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. 20m
- B. 25m
- C. 22.5m
- D. 9m Discuss
Correct Answer: 20m
Explanation:
Distance covered by B in 9 sec. = (100/45)*9m = 20m
A beats B by 20 metres.
- 2. 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. 60m
- B. 40m
- C. 20m
- D. 10m Discuss
Correct Answer: 20m
Explanation:
To 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 (4/3)*360 = 480 m.
Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.
A wins by 20 m.
- 3. 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. 47sec
- C. 33sec
- D. none of these Discuss
Correct Answer: 33sec
Explanation:
B runs 35 m in 7 sec.
B covers 200 m in (7/35*200) = 40 sec.
B's time over the course = 40 sec.
A's time over the course (40 - 7) sec = 33 sec.
- 4. 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/C = (B/A*A/C) = (45/60*60/45) = 45/40 = 90/80 = 90:80
B can give C 10 points in a game of 90.
- 5. In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m ?
Options- A. 127.5 m
- B. 254 m
- C. 184 m
- D. 212 m Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 127.5 m
Explanation:
When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C
= (600 x 212.5)/1000 = 127.5 m.
- 6. A runs 123 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. 300m
- C. 270m
- D. 160m Discuss
Correct Answer: 200 m
Explanation:
Ratio of the speeds of A and B =5 : 1 = 5 :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 m =200m
=> Winning post is 200 m away from the starting point.
- 7. 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. 18.5 m Discuss
Correct Answer: 25 m
Explanation:
A : B = 200 : 169.
A : C = 200 : 182.
C/B = (C/A*A/B) = (182/200*200/169) = 182:169
When C covers 182 m, B covers 169 m.
When C covers 350 m, B covers (169/180*350)m = 325 m
Therefore, C beats B by (350 - 325) m = 25 m.
- 8. 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. 28m
- D. 29m Discuss
Correct Answer: 28m
- 9. In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C is
Options- A. 8 points
- B. 10 points
- C. 14 points
- D. 40 points Discuss
Correct Answer: 10 points
- 10. In a race of 1000 meters, A can beat B by 100 meters, in a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters?
Options- A. 125.5 meters
- B. 126.5 meters
- C. 127.5 meters
- D. 128.5 meters Discuss
Correct Answer: 127.5 meters
Explanation:
When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters.
Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters.
So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C.
So, in a race of 600 meters, the number of meters by Which A beats C = (600 x 212.5)/1000 = 127.5 meters.
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