Races and Games problems
- 1. A runner runs 1 1? 4 laps of a 5 lap race. What fractional part of the race remains to be run?
Options- A. 15?4
- B. 4?5
- C. 5?6
- D. 2?3 Discuss
Correct Answer: 15?4
Explanation:
race remains to be run = 5 - 5?4 = 15?4 .
- 2. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet next at the starting point again?
Options- A. 46 minutes 12 seconds
- B. 45 minutes
- C. 42 minutes 36 seconds
- D. 26 minutes 18 seconds Discuss
Correct Answer: 46 minutes 12 seconds
Explanation:
L.C.M. of 252, 308 and 198 = 2772 seconds
= 46 × 60 + 12 = 46 min 12 seconds.
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- 3. Raju runs 1250 meter on Monday and Friday. Another days he runs 1500 meter except for Sunday (He does not run on Sunday). How many kilometer will he run in 3 weeks (first day starting from Monday)?
Options- A. 12.5 Km
- B. 20.5 Km
- C. 8.5 Km
- D. 25.5 Km Discuss
Correct Answer: 25.5 Km
Explanation:
Raju runs on Monday and Friday = 1250 × 2 = 2500 m
On Tuesday, Wednesday, Thursday and Saturday,
Raju runs 1500 × 4 = 6000 m
In 1 week Raju runs 6000 + 2500 = 8500 m
In 3 weeks Raju runs 3 × 8500 = 25500 m = 25.5 K
- 4. In a race of 300 meter, A beats B by 15 meter or 5 sec. A's time over the course is :
Options- A. 100 seconds
- B. 95 seconds
- C. 105 seconds
- D. 90 seconds Discuss
Correct Answer: 95 seconds
Explanation:
15 meter is covered by B in 5 sec
? 300 meter is covered by B in 5 × 300/15 = 100 seconds
? A takes 100 - 5 = 95 seconds.
- 5. A runs 1 3? 8 times as fast as B. If A gives B a start of 120 m and they reach the goal at the same time, the goal is at a distance of:
Options- A. 360 m
- B. 440 m
- C. 460 m
- D. 380 m Discuss
Correct Answer: 440 m
Explanation:
The speed of A and B are in the ratio 11 : 8.
Let, speeds be 11s and 8s (in m/sec).
Let, race be of P meter.
Then, time taken by A to run P meter is same as that of B to run (P - 120) meter.
? P / 11 = (P - 120) / 8
? P / 11 = (P - 120 / 8
? 8P = 11 x (P - 120 )
? 8P = 11P - 120 x 11
? 11P - 8P = 120 x 11
? 3P = 11 × 120
? P = 440.
- 6. At a game of billiards, A can give B 6 points in 50 and he can give C 13 in 65. In a game of 55, number of points B can give C is:
Options- A. 3
- B. 4
- C. 5
- D. 8 Discuss
Correct Answer: 5
Explanation:
In a game of 50.
While A scores 50, B scores 50 - 6 = 44 and in a game of 65. While A scores 65, C scores 65 - 13 = 52.
? While A scores 50, C scores 52 / 65 × 50 = 40.
? While B scores 44, C's score = 40.
While B scores 55, C's score = 40 / 44 × 55 = 50.
? In a game of 55,
B can give C 55 - 50 = 5 points.
- 7. In a race of 600 m, A can beat B by 30 m and in a race of 500 m, B can beat C by 25 m. By how many metres will A beat C in a race of of 400 m?
Options- A. 39 m
- B. 49 m
- C. 55 m
- D. 25 m Discuss
Correct Answer: 39 m
Explanation:
If A runs 600 m, then B runs 570 m.
If A runs 400 m, B then runs (570/600) x 400 m = 380 m
When B runs 500 m, then C runs 475 m,
When B runs 380 m, then C runs (475/500) x 380 = 361 m
? A beats C by (400 - 361) = 39 m
- 8. A runs 1% times as fast as B. If A gives B a start of 30 m, how far must the winning post be, so that A and B reach it at the same time?
Options- A. 52 m
- B. 75 m
- C. 69 m
- D. 70 m Discuss
Correct Answer: 70 m
Explanation:
A is 13/4 faster than B.
Then, ratio of the rates of A and B = 7 : 4
3 m are gained in a race of 7 m .
30 m are gained in a race of (7/3) x 30 = 70 m
- 9. In a 250 m race, the ratio of speeds of A and B is 1 : 2, If A has a start of 140 m, then A wins by how many metres?
Options- A. 45 m
- B. 15 m
- C. 25 m
- D. 30 m Discuss
Correct Answer: 30 m
Explanation:
To reach the winning post, A has to cover (250 - 140)m = 110 m
From the the ratio of 1 : 2 ,
When A covers 1m, then B covers 2 m.
When A covers 110 m, then B covers
( 2 x 110)m = 220 m
? A wins by (250 - 220) = 30 m
- 10. In 1 km race, P beats Q by 72 m in 12 s. Find the P's time over the course.
Options- A. 1552/3 s
- B. 151 s
- C. 1542/3 s
- D. 160 s Discuss
Correct Answer: 1542/3 s
Explanation:
According to the formula,
Time taken by the winner/Distance covered by the loser = Difference of winning time/ Difference of winning distance
? Time taken by P//(1000 - 72) = 12/72
? Time taken by P = (12/72) x 928
= 464/3 = 1542/3 s
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