Races and games

Races and games

1. In a race of 300 meter, A beats B by 15 meter or 5 sec. A’s time over the course is :
1. 100 seconds
2. 95 seconds
3. 105 seconds
4. 90 seconds

1. 15 meter is covered by B in 5 sec .
∴ 300 meter is covered by B in 5 × 300/15 = 100 seconds

Correct Option: B

15 meter is covered by B in 5 sec
∴ 300 meter is covered by B in 5 × 300/15 = 100 seconds
A takes 100 - 5 = 95 seconds.

1. A runs 138 times as fast as B. If A gives B a start of 120 m and they reach the goal at the same time, the goal is at a distance of:
1. 360 m
2. 440 m
3. 460 m
4. 380 m

1. The speed of A and B are in the ratio 11 : 8.
Let, speeds be 11s and 8s (in m/sec).
Let, race be of P meter.

Correct Option: B

The speed of A and B are in the ratio 11 : 8.
Let, speeds be 11s and 8s (in m/sec).
Let, race be of P meter.
Then, time taken by A to run P meter is same as that of B to run (P - 120) meter.
∴ P / 11 = (P - 120) / 8
∴ P / 11 = (P - 120 / 8
∴ 8P = 11 x (P - 120 )
∴ 8P = 11P - 120 x 11
∴ 11P - 8P = 120 x 11
∴ 3P = 11 × 120
∴ P = 440.

1. At a game of billiards, A can give B 6 points in 50 and he can give C 13 in 65. In a game of 55, number of points B can give C is:
1. 3
2. 4
3. 5
4. 8

1. In a game of 50.
While A scores 50, B scores 50 - 6 = 44 and in a game of 65. While A scores 65, C scores 65 - 13 = 52.

Correct Option: C

In a game of 50.
While A scores 50, B scores 50 - 6 = 44 and in a game of 65. While A scores 65, C scores 65 - 13 = 52.
∴ While A scores 50, C scores 52 / 65 × 50 = 40.
∴ While B scores 44, C’s score = 40.
While B scores 55, C’s score = 40 / 44 × 55 = 50.
∴ In a game of 55,
B can give C 55 - 50 = 5 points.