Aptitude - Races and Games

Exercise : Races and Games - General Questions
1.
In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:
18 m
20 m
27 m
9 m
Explanation:

A : B = 100 : 90.

A : C = 100 : 72.

 B : C = B x A = 90 x 100 = 90 . A C 100 72 72

When B runs 90 m, C runs 72 m.

 When B runs 100 m, C runs 72 x 100 m = 80 m. 90

B can give C 20 m.

2.
A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:
5.15 kmph
4.14 kmph
4.25 kmph
4.4 kmph
Explanation:

 A's speed = 5 x 5 m/sec = 25 m/sec. 18 18

 Time taken by A to cover 100 m = 100 x 18 sec = 72 sec. 25

Time taken by B to cover 92 m = (72 + 8) = 80 sec.

 B's speed = 92 x 18 kmph = 4.14 kmph. 80 5

3.
In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
60 m
40 m
20 m
10 m
Explanation:

To reach the winning post A will have to cover a distance of (500 - 140)m, i.e., 360 m.

While A covers 3 m, B covers 4 m.

 While A covers 360 m, B covers 4 x 360 m = 480 m. 3

Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.

A wins by 20 m.

4.
In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:
5.4 m
4.5 m
5 m
6 m
Explanation:

A : B = 100 : 90.

A : C = 100 : 87.

 B = B x A = 90 x 100 = 30 . C A C 100 87 29

When B runs 30 m, C runs 29 m.

 When B runs 180 m, C runs 29 x 180 m = 174 m. 30

B beats C by (180 - 174) m = 6 m.

5.
At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?
30 points
20 points
10 points
12 points