Races and Games problems
- 1. X covers 1 km in 8 min 40 s while Y covers the same distance in 10 min. By what distance does X defeat Y?
Options- A. 131/3 m
- B. 1332/3 m
- C. 1332/5 m
- D. 1331/3 m Discuss
Correct Answer: 1331/3 m
Explanation:
Clearly, X beats Y by 8 s.
Distance covered by Y in 600 s = 1000 m
(? 10 min = 600 s)
Distance covered by Y 80 s. = (1000/600) x 80 = 400/3 m = 1331/3 m
- 2. L can run 1 km in 10 min while M can run it in 12 min. How many metres start can L give M in a km race, so that the race may end in a dead heat?
Options- A. 1662/3 m
- B. 1661/3 m
- C. 1663/5 m
- D. 200 m Discuss
Correct Answer: 1662/3 m
Explanation:
Time taken by L to run 1 km = 600 s
Time taken by M to run 1 km = 720 s
? L can give M a start of (720 - 600) = 120 s
? In 720 s, M runs 1000 m.
In 120 s M runs = (1000/720) x 120 = 500/3 m = 1662/3 m
Hence, L can give a start of 1662/3 m
- 3. Yogesh can run 1km in 6 min 20 s and Vijay can cover the same distance in 6 min 40 s . By what distance can Yogesh beat Vijay?
Options- A. 50 m
- B. 90 m
- C. 45 m
- D. 30 m Discuss
Correct Answer: 50 m
Explanation:
Clearly, Yogesh beats vijay by 20 s.
Distance covered by vijay in 400 s = 1000 m
[? 6 min 40 s = 400 s]
Distance covered by Vijay in 20 s = (1000/400) x 20 m = 50 m
? Yogesh beats Vijay by 50 m.
- 4. In a game of 160 points, A can give 10 points to B and 30 points to C. How many points B can give C in a game of 60?
Options- A. 10
- B. 15
- C. 6
- D. 8 Discuss
Correct Answer: 8
Explanation:
A : B = 160 : 150, A : C =160 : 130
B/C = (B/A) x (A/C) = (150/160) x (160/130) = 15/13 = 60 : 52
? In a game of 60, B can give C = (60 - 52)= 8 points
- 5. In a 200 m race, A can beat B by 50 m and B can beat C by 8 m. In the same race , A can beat C by what distance?
Options- A. 60 m
- B. 72 m
- C. 56 m
- D. 66 m Discuss
Correct Answer: 56 m
Explanation:
According to the question, A : B = 200 : 150
and B : C = 200 : 192
? A : C = (A/B) x (B/C) = (200/150) x (200/192) = 200/144
So, A beats C by (200 - 177) = 56 m
- 6. In a game of 200 points, A can give 40 points to B and 56 points to C. How many points can B give to C?
Options- A. 20 points
- B. 15 points
- C. 10 points
- D. 5 points Discuss
Correct Answer: 20 points
Explanation:
A : B = 200 : 160
A : C = 200 : 144
? B/C = (B/A) x (A/C) = (160/200) x (200/144)
= 160/144 = 10/9 = 200/180
Hence, B can give C 20 points
- 7. A can run 100 metres in 27 seconds and B in 30 seconds. A will beat B by
Options- A. 12 m
- B. 111?8 m
- C. 10 m
- D. 9 m Discuss
Correct Answer: 10 m
Explanation:
Distance covered by B in 27 seconds = 100 x 27 / 30 = 90 m
Hence, A will beat B by (100 ? 90) = 10 m.
- 8. A can run 440 m in 51 seconds and B in 55 seconds. By how many seconds will B win if he has 40 m start?
Options- A. 1 seconds
- B. 2 seconds
- C. 3 seconds
- D. 4 seconds Discuss
Correct Answer: 1 seconds
Explanation:
To reach the winning post B will have to cover the distance (440 ? 40) = 400 m.
Hence,
time taken by B to cover 440 meter = 55
time taken by B to cover 1 meter = 55 / 440
time taken by B to cover 400 meter = 400 x 55 / 440 = 40 x 55/44 =10 x 55/11 = 10 x 5
time taken by B to cover 400 meter = 50 Sec.
Since, A reaches the winning post in 51 sec. while B in 50 sec.
So, B will win by 1 second.
- 9. In a km race A can give B 50 m start and B can give C 40 m start. What start can A give C in a 2 km race?
Options- A. 222 m
- B. 220 m
- C. 167 m
- D. 176 m Discuss
Correct Answer: 176 m
Explanation:
? B runs 1000 m while C 960 m
? B runs 995 m while C 960 * 995 / 1000 = 912 m
Now, A runs 1000 m while C 960 m
? A runs 2000 m while C 2000 * 912 / 1000 = 1824 m
Hence, A can give C (2000 ? 1824) = 176 m start.
- 10. A can give B 40 m and C 82 m in a 880 m race while B can give C 9 seconds over the post, find the time C takes to run 880 m.
Options- A. 3.25 min.
- B. 3 min.
- C. 4 min.
- D. None of these Discuss
Correct Answer: 3 min.
Explanation:
If A runs 880 meter then B runs 840 meters and C runs 798 meters.
? B runs 840 m while C 798 m
? B runs 880 m while C 798 * 880 / 840 = 836 m
Now, 880 ? 836 = 44 m
Hence, C runs 44 m in 9 seconds
? C runs 880 m in 9 * 880 / 44 = 180 sec. = 3 min.
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