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- Question
- A and B run a 5 Km race on a round course of 400 m. If their speeds be in the ratio 5 : 4, then how often does the winner pass the other?
Options- A. 41?2 times
- B. 31?2 times
- C. 23?4 times
- D. 21?2 times
- Correct Answer
- 21?2 times
ExplanationWhen A makes 5 rounds, B makes 4 rounds.
In order to pass each other, the difference in number of rounds made by each must be one.
Here, A passes B each time, when A makes 5 rounds.
Distance covered by A in 5 rounds = 5 * 400 / 100 × = 2 Km.
In covering 2 Km, A passes B 1 time.
? In covering 5 Km, A passes B
= 5 / 2 = 21?2 times. - 1. In a Km race A can beat B by 80 m and B can beat C by 60 m. In the same race, A can beat C by :
Options- A. 135.2 m
- B. 130.5 m
- C. 142 m
- D. 132.5 m Discuss
- 2. A's speed is 1 3? 8 times of B's. In a race A gives B a start of 300 m. How long should the race course be so that both reach the winning post simultaneously?
Options- A. 700 m
- B. 900 m
- C. 800 m
- D. 850 m Discuss
- 3. A can run 500m in 30 seconds and B in 35 seconds. How many meter start can A give to B in a Km race so that the race may end in a dead-heat?
Options- A. 1395?7
- B. 1385?7
- C. 1426?7
- D. 1405?7 Discuss
- 4. In a race of 200 metres, B can give a start of 10 metres to A and C can give a start of 20 metres to B. The start that C can give to A, in the same race, is
Options- A. 30 m
- B. 29 m
- C. 27 m
- D. 25 m Discuss
- 5. At a game of billiards A can give B 6 points in 50 and he can give C 13 points in 65, how many points can B give C in a game of 55?
Options- A. 7
- B. 8
- C. 5
- D. 10 Discuss
- 6. A and B runs a Km race. If A gives B a start of 50 m, A wins by 14 sec and, if A gives B a start of 22 sec Km, B wins by 20 m. The time taken by A to run a Km is:
Options- A. 100 sec
- B. 120 sec
- C. 105 sec
- D. 125 sec Discuss
- 7. A and B start from the same point and run around a circular stadium, whose circumference is 4200 m, at the rate of 500 m and 700 m per minute respectively, in the opposite directions. They will meet each other in :
Options- A. 3.5 minutes
- B. 6.0 minutes
- C. 8.4 minutes
- D. 21 minutes Discuss
- 8. In a game of 100 points, A can give B 20 points and C 28 points. Number of points B can give C in a game of 100 points is:
Options- A. 10
- B. 90
- C. 15
- D. 85 Discuss
- 9. In a game of 90 points, A can give B 15 points and C 30 points. How many points can B give C in a game of 100 points?
Options- A. 140
- B. 20
- C. 50
- D. 30 Discuss
- 10. The respective ratio between the speeds of a car, a train and a bus is 5 : 9 : 4. The average speed of the car, the bus and the train is 72 Km/h together. What is the average speed of the car and the train together?
Options- A. 82 km/h
- B. 78 km/h
- C. 84 km/h
- D. Cannot be determined Discuss
Races and Games problems
Search Results
Correct Answer: 135.2 m
Explanation:
While A runs 1000 m, B runs 1000 - 80 = 920 m and
While B runs 1000 m, C runs 1000 - 60 =940 m.
? While B runs 920 m; C runs
940 / 1000 × 920 = 4324 / 5 m
? While B runs 920 m; C runs 940 × 920 / 1000 = 4324 / 5 m
? While A runs 1000 m, C runs 4324 / 5 m
? A can beat C by 1000 - 4324 / 5 = 676 / 5 = 1351?5 m.
Correct Answer: 900 m
Explanation:
A's speed : B's speed = 11?2 : 1
= 3?2 : 1
= 3 : 2
It means that in a race of 3 m, A gains (3 - 2).
= 1 m over B. 1 m is gained by A in a race of 3 m.
? 300 m is gained by A in a race of = 3?1 × 300 = 900 m.
Correct Answer: 1426?7
Explanation:
Time taken by A to run 1 Km = 30 × 2 = 60 seconds.
Time taken by B to run 1 Km = 35 × 2 = 70 seconds.
? A can give B a start of (70 - 60) = 10 seconds.
In 35 sec B runs 500 m
? In 10 sec B runs = 500 × 10 / 35 = 1000 / 7 = 1426?7 meters
So, A can give B a start of 1426?7 meters in a Km race.
Correct Answer: 29 m
Explanation:
B covers 200 m while A 190 m
B covers 180 m while A 190 x 180 / 200 = 171 m
Hence, C covers 200 m while A = 171 m
So, C can give to A (200 ? 171) = 29 m start.
Correct Answer: 5
Explanation:
In a game of 50, If A scores 50 then B scores 44.
? A scores 65 while B 44 * 65 / 50 = 57.2 points
Now, B scores 57.2 points while C 52
? B scores 55 points while C = 52 * 55 / 57.2 = 50
Hence, in game of 55 points B can give C (55 ? 50) = 5 points
Correct Answer: 100 sec
Explanation:
Let, times (in sec) taken by A and B to run a Km, be P and Q, respectively.
When B gets a start of 50 m, B runs.
1000 - 50 = 950 m while A runs 1000 m.
? 950 / 100 Q - P = 14,
i.e., 0.95Q - P = 14 ?(1)
and, when B gets a start of 22 seconds, A runs for (Q - 22) seconds, while B runs for Q seconds.
? 1000 - 1000 / P (Q - 22) = 20
i.e., 50Q - 49P = 1100. ?(2)
Multiplying Eq. (1) by 49 and subtract from Eq. (2)
3.45Q = 414
? Q= 120 sec.
? from (1)
? P = 0.95 × 120 - 14 = 100 seconds.
Correct Answer: 3.5 minutes
Explanation:
Let us assume A cover P meter in the time after which he meets with B.
According to question,
Time taken by A to cover the P distance = Time taken by B to cover the 4200 - P distance.
Use the distance and time formula
P / 500 = (4200 - P ) / 700
Or 700P = 500 x 4200 - 500P
Or 700P + 500P = 500 x 4200
Or 1200P = 500 x 4200
Or 12P = 5 x 4200
Or P = 5 x 4200 / 12
Or P = 5 x 350
Or P = 1750 meters
Required time taken by A to cover 1750 meters = 1750 / 500 = 175/50
Required time taken by A to cover 1750 meters = 3.5 minutes.
Correct Answer: 10
Explanation:
A scores 100 while B scores 100 - 20 = 80 and C scores 100 - 28 = 72.
? While B scores 80, C scores 72.
? While B scores 100, C scores 72 × 100 / 80 = 90.
? B can give C 100 - 90 = 10 points.
Correct Answer: 20
Explanation:
A : B : C = 90 : 75 : 60
B:C = 75 / 60 = ( 75 x 100?75 ) / ( 60 x 100?75) = 100 / 80
Hence, in a game of 100 points, B can give C(100 - 80)
= 20 points.
Correct Answer: 84 km/h
Explanation:
Total speed of car, bus and train = 72 × 3 = 216 Km
Speed of car and train = ( 5 + 9 ) x 216 / ( 5 + 9 + 4 ) = 168 Km
Average = 168 / 2 = 84 Km
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