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- Question
- Two men A and B run a 500 m race, A having 140 m start, their speeds are as 3 : 4. Then, A wins by :
Options- A. 10 m
- B. 20 m
- C. 40 m
- D. 60 m
- Correct Answer
- 20 m
ExplanationHere, A will have to cover a distance of (500 ? 140) = 360 meters to reach the winning point while B 500 meters . A covers 3 while B covers 4.
? A covers 360 m while B covers 4 x 360/ 3 = 480 m
Hence, B will be (500 ? 480) = 20 m behind the winning post.
? A wins by 20 m. - 1. In a game of 80 points, A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60?
Options- A. 12
- B. 10
- C. 8
- D. 6 Discuss
- 2. A can give B 15 points, A can give C 22 points and B can give C 10 points. How many points make the game?
Options- A. 50
- B. 60
- C. 70
- D. 80 Discuss
- 3. 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
- 4. 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
- 5. 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
- 6. In a race of 600 m, A can beat B by 60 m and in a race of 500 m, B can beat C by 50 m. By how many meters will A beat C in a race of 400 m?
Options- A. 364 m
- B. 254 m
- C. 324 m
- D. 354 m Discuss
- 7. In a race of 600 m, A can beat B by 60 m and in a race of 500 m, B can beat C by 50 m. By how many meter will A beat C in a race of 400 m?
Options- A. 78 m
- B. 56 m
- C. 76 m
- D. 86 m Discuss
- 8. In a game A can give B 25 points in 75 and C 18 points in 90. How many points can C give B in a game of 120?
Options- A. 20
- B. 30
- C. 40
- D. 50 Discuss
- 9. In a 500 m race, the ratio of speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
Options- A. 60 m
- B. 40 m
- C. 20 m
- D. 10 m Discuss
- 10. Two boys, A and B, runs at 4 1? 2 and 6 Km an hour. A having 190 m start. The course being 1 Km, B wins by a distance of :
Options- A. 60 m
- B. 65 m
- C. 45 m
- D. 75 m Discuss
Races and Games problems
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Correct Answer: 8
Explanation:
? B scores 75 points while A 80
? B scores 60 points while A = 80 x 60 / 75 = 64
Again, A scores 80 points while C = 65
? A scores 64 points while C = 65 x 64 / 80 = 52 points
Hence, in a game of 60, B can give C (60 ? 52) = 8 points
Correct Answer: 50
Explanation:
Let assume the game has P points.
Then A has P points , B has (P ? 15) and C has (P ? 22) points and also if B has P points then C has (P ? 10) points.
Applying chain rule,
P x P ( P ? 22 ) = P ( P ? 15) ( P ? 10)
? P2 ? 22P = P2 ? 25P + 150
? 3P = 150
? P = 50
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.
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.
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.
Correct Answer: 324 m
Explanation:
Clearly, if A runs 600 meters, B runs = 540 m.
? If A runs 400 m, B runs = 540 x 400 / 600 = 540 x 4 / 6 = 90 x 4 = 360 m
Again, when B runs 500 m, C runs = 450 m
? When B runs 360 m, C runs = 450 x 360 / 500 = 45 x 36 / 5 = 9 x 36 = 324 m.
? A beats C by 400 - 324 = 76 m.
Correct Answer: 76 m
Explanation:
If A runs 600 m, B runs 600 - 60 or, 540 m.
If A runs 400 m, B runs = 540 x 400 / 600 = 360 m.
Now, when B runs 500 m, C runs 500 - 50 = 450 m.
? When B runs 360 m, C runs = 450 * 360 / 500 = 324 m
? A beats C by 400 - 324 = 76 m.
Correct Answer: 20
Explanation:
When A scores 75 points, B scores 50 points.
When A scores 90 points, C scores (90 - 18) = 72 points.
? When A scores 75 points, C scores = 72 × 75 / 90 = 60 points.
A : B : C = 75 : 50 : 60
C : B = 60 / 50 = 120 / 100
So, in a game of 120, C can give B
(120 - 100) = 20 points.
Correct Answer: 20 m
Explanation:
To reach the winning post, A will have to cover a distance of (500 - 140). i.e, 360 m.
While A covers 3 m, B covers 4 m.
While A covers 360 m, B covers 4 × 360 / 3 = 480 m.
So, A reaches the winning post while B remains 20 meter behind.
? A wins by 20 m.
Correct Answer: 60 m
Explanation:
Speeds (in m/sec) of A and B are
9 / 2 * 5 / 18 = 5 / 4 and 6 * 5 / 18 = 5 / 3, respectively.
A has a start of 190 m.
So, A has to run 1000 - 190 = 810 m, while B 1000 m.
Time taken by B to cover 1000 m = 3 5 × 1000 = 600 seconds.
In this time, A covers 5 × 600 / 4 = 750 m.
So, B reaches the winning post while A remains 810 - 750 = 60 m behind.
? B wins by 60 m.
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