Races and games
- 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?
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When 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.Correct Option: D
When 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.
- 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:
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A scores 100 while B scores 100 - 20 = 80 and C scores 100 - 28 = 72.
∴ While B scores 80, C scores 72.Correct Option: A
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.
- 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?
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Total speed of car, bus and train = 72 × 3 = 216 Km
Speed of car and train = ( 5 + 9 ) x 216 / ( 5 + 9 + 4 ) = 168 KmCorrect Option: C
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
- 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?
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A:B:C = 90:75:60
B : C = 75 / 60 = ( 75 x 100⁄75 ) / ( 60 x 100⁄75) = 100 / 80Correct Option: B
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.
- 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?
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In a game of 50, If A scores 50 then B scores 44.
∴ A scores 65 while B 44 * 65 / 50 = 57.2 pointsCorrect Option: C
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