Races and Games problems
- 1. In a 400 m race, A runs at a speed of 16 m/s. If A gives B a start of 16 m and still beats him by 40 s, What will be the speed of B?
Options- A. 6 m/s
- B. 8 m/s
- C. 15 m/s
- D. 5.9 m/s Discuss
Correct Answer: 5.9 m/s
Explanation:
Time taken by A to cover 400 m = Distance/ Speed
= 400/16 s = 25 s
? B covers (400 -16) = 384 m in(25 + 40) = 65 s
? B's speed = 384/65 =5.9 m/s
- 2. A can run 45 m while B runs 50 m. In a km race B beats A by how many metres?
Options- A. 150 m
- B. 200 m
- C. 100 m
- D. 125 m Discuss
Correct Answer: 100 m
Explanation:
When B runs 50 m, then A runs 45 m.
When B runs 1000 m, then A runs (45/50) x 1000 m = 900 m
? B beats A by 100 m.
- 3. A can run 200 m in 35 seconds and B in 38 seconds. By what distance A beats B?
Options- A. 15 m
- B. 152?3 m
- C. 1515?19 m
- D. 154?19 m Discuss
Correct Answer: 1515?19 m
Explanation:
The distance covered by B in 35 seconds = 200 x 35 / 38 = 3500 / 19 m
Now, 200 ? 3500 / 19 = 300 / 19 = 1515?19 m Hence, A can beat B by 1515?19 m.
- 4. In a 1000 m race A beats B by 100 m and C by 200 m. By how much can B beats C in a race of 1350 m?
Options- A. 125 m
- B. 130 m
- C. 140 m
- D. 150 m Discuss
Correct Answer: 150 m
Explanation:
If A run 1000 meters then B runs 900 meters and C runs 800 meters.
? B runs 1350 meters while C will run 800 * 1350/ 900 = 1200 meters
Hence, B can beat C by (1350 ? 1200) = 150 m
- 5. In a game of 100 points A can give B 20 points and C 28 points. How many points can B give C in a game of 100 points?
Options- A. 12 points
- B. 15 points
- C. 20 points
- D. 10 points Discuss
Correct Answer: 10 points
Explanation:
If A Score 100 then B scores 80 and C score 72.
? B scores 80 while C scores 72
? B scores 100 while C scores 72 * 100 / 80 = 90 points
Hence, in 100 points B can give (100 ? 90) = 10 points
- 6. A can give B 50 m start and C 80 m start in the 1000 m race, how many metres start B give C in a 1000 m race?
Options- A. 31 m
- B. 3111?19 m
- C. 312?19 m
- D. 3011?19 m Discuss
Correct Answer: 3111?19 m
Explanation:
In a game of 1000 meters, If A scores 1000 meters then B scores 950 meters and C scores 920 meters.
? B runs 1000 m while C scores 920 x 1000 / 950= 18400 / 19 m
Hence, in 1000 m race, B can give C (1000 - 18400 / 19) = 600 / 19 = 3111?19 meters start.
- 7. In a game of 250 points A can give B 50 points and C 70 points. In the same game how many points can B give C?
Options- A. 18 points
- B. 20 points
- C. 22 points
- D. 25 points Discuss
Correct Answer: 25 points
Explanation:
In a game of 250 points, A scores 250 then B scores 200 points and C scores 180.
? B scores 250 points while C scores 180 x 250 / 200 = 225 points
Hence, in a game of 250 points B can give C (250 ? 225) = 25 points
- 8. In a race of 300 metres A beats B by 15 metres or 5 seconds. How much time A does take to complete the race?
Options- A. 105 sec.
- B. 100 sec.
- C. 95 sec.
- D. 90 sec. Discuss
Correct Answer: 95 sec.
Explanation:
From the question it is clear that speed of B = 15 / 5 = 3 m/s
The time taken by B to cover 300 m = 300 / 3 = 100 sec.
Hence, time taken by A to complete the race = 100 ? 5 = 95 sec.
- 9. In a Km race A beats B by 25 m or 5 sec. Then find out the time taken by A to complete the race.
Options- A. 3 minutes 15 seconds
- B. 4 minutes 20 seconds
- C. 2 minutes 30 seconds
- D. 5 minutes 10 seconds Discuss
Correct Answer: 3 minutes 15 seconds
Explanation:
B runs 25 m in 5 seconds.
? B's time to cover 1 Km = 5 x 100 / 25 = 200 sec
A's time to cover one Km = 200 - 5 = 195 seconds
= 3 minutes 15 seconds.
- 10. In a game, A can give B 20 points, A can give C 32 points and B can give C 15 points. How many points make the game?
Options- A. 100
- B. 200
- C. 300
- D. 400 Discuss
Correct Answer: 100
Explanation:
Suppose, P points make the game.
Clearly, when A scores P points, B scores (P - 20) points and C scores (P - 32) points.
Now, when B scores P points, C scores (P - 15) points.
When B scores (P - 20) points,
C scores [( P - 15 ) / P * P (P - 20)] points
? (P - 15)( P - 20) / P = P - 20 or, P = 100
Hence, 100 points make the game.
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