## Races and games

#### Races and games

1. 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?

1. 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.

##### Correct Option: C

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.

1. 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?

1. 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.

##### Correct Option: A

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.

1. 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.

1. B runs 25 m in 5 seconds.
∴ B’s time to cover 1 Km = 5 x 100 / 25 = 200 sec

##### Correct Option: A

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.

1. A runner runs 114 laps of a 5 lap race. What fractional part of the race remains to be run?

1. race remains to be run = 5 - 54

##### Correct Option: A

race remains to be run = 5 - 54 = 154 .

1. 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?

1. In a game of 250 points, A scores 250 then B scores 200 points and C scores 180.

##### Correct Option: D

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