Races and Games Questions and Answers
Practice ModeShowing 10 of 37 questions
Q21
In a race of 600m, A can beat B by 60m and in a race of 500m, B can beat C by 50m. By how many meters will A beat C in a race of 400m?
Answer: Option B
Explanation: A:B = 600:540 = 10:9, B:C = 500:450 = 10:9. A:C = 10/9 × 10/9 = 100:81. In 400m race, when A runs 400m, C runs 400 × 81/100 = 324m. So A beats C by 76m.
Q22
In a 200m race, A beats B by 20m or 4 seconds. What is A's speed?
Answer: Option B
Explanation: B covers 20m in 4 seconds, so B's speed = 5 m/s. When A finishes 200m, B covers 180m in 180/5 = 36 seconds. So A's time = 36 seconds, speed = 200/36 = 5.56 m/s.
Q23
A can give B 100m start and C 150m start in a km race. How many meters start can B give C?
Answer: Option C
Explanation: A:B = 1000:900 = 10:9, A:C = 1000:850 = 20:17. B:C = 9/10 × 20/17 = 180/170 = 18:17. So in 1000m, B can give C 1000 - (1000 × 17/18) = 55.56m ≈ 56m.
Q24
In a game of 80 points, A can give B 10 points and C 16 points. How many points can B give C?
Answer: Option B
Explanation: A:B = 80:70 = 8:7, A:C = 80:64 = 5:4. B:C = 7/8 × 5/4 = 35/32 = 35:32. So B can give C 3 points in 35, or (3/35)×80 ≈ 7 points in 80.
Q25
Two athletes A and B are running around a circular track of length 400m. They start simultaneously from the same point. If their speeds are 10 m/s and 8 m/s, after how much time will they meet at the starting point for the first time?
Answer: Option B
Explanation: Time taken by A for one lap = 400/10 = 40s. Time taken by B for one lap = 400/8 = 50s. They meet at starting point at LCM(40,50) = 200 seconds.
Q26
In a 100m race, A beats B by 10m. B beats C by 10m. What is the ratio of speeds of A, B and C?
Answer: Option B
Explanation: A:B = 100:90 = 10:9, B:C = 100:90 = 10:9. So A:B:C = 100:90:81 (multiplying A:B and B:C ratios).
Q27
A runs 5/4 times as fast as B. In a race, A wins by 50m. What is the length of the race?
Answer: Option B
Explanation: Speed ratio A:B = 5:4. Let race length be x. Then (x-50)/4 = x/5. Solving: 5x-250 = 4x, x = 250m.
Q28
In a 400m race, A beats B by 40m. B beats C by 40m. By what distance does A beat C?
Answer: Option B
Explanation: A:B = 400:360 = 10:9, B:C = 400:360 = 10:9. A:C = 10/9 × 10/9 = 100:81. When A runs 400m, C runs 400 × 81/100 = 324m. So A beats C by 76m.
Q29
In a race of 600m, A can beat B by 30m and in a race of 500m, B can beat C by 25m. By how many meters will A beat C in a race of 400m?
Answer: Option B
Explanation: A:B = 600:570 = 20:19, B:C = 500:475 = 20:19. A:C = 20/19 × 20/19 = 400:361. In 400m race, when A runs 400m, C runs 400 × 361/400 = 361m. So A beats C by 39m.
Q30
A and B run a 500m race. A wins by 25m. What is the ratio of their speeds?
Answer: Option A
Explanation: When A runs 500m, B runs 475m. Ratio of speeds = 500:475 = 20:19.