## 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?

Question:
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?

[A].

30 points

[B].

20 points

[C].

10 points

[D].

12 points

Explanation:

A : B = 60 : 45.

A : C = 60 : 40.

 B = B x A = 45 x 60 = 45 = 90 = 90 : 80. C A C 60 40 40 80

B can give C 10 points in a game of 90.

## In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:

Question:
In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:

[A].

8 points

[B].

10 points

[C].

14 points

[D].

40 points

Explanation:

A : B = 100 : 80.

A : C = 100 : 72.

 B = B x A = 80 x 100 = 10 = 100 = 100 : 90. C A C 100 72 9 90

B can give C 10 points.

## 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:

Question:
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:

[A].

5.15 kmph

[B].

4.14 kmph

[C].

4.25 kmph

[D].

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

## In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:

Question: In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:

[A].

22.75 m

[B].

25 m

[C].

19.5 m

[D].

 7 4 m 7

Explanation:

A : B = 200 : 169.

A : C = 200 : 182.

 C = C x A = 182 x 200 = 182 : 169. B A B 200 169

When C covers 182 m, B covers 169 m.

 When C covers 350 m, B covers 169 x 350 m = 325 m. 182

Therefore, C beats B by (350 – 325) m = 25 m.

## 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:

Question:
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:

[A].

5.4 m

[B].

4.5 m

[C].

5 m

[D].

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.

## In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:

Question:
In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:

[A].

18 m

[B].

20 m

[C].

27 m

[D].

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.

## In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:

Question:
In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:

[A].

21 m

[B].

26 m

[C].

28 m

[D].

29 m

Explanation:

A : B = 100 : 75

B : C = 100 : 96.

 A : C = A x B = 100 x 100 = 100 = 100 : 72. B C 75 96 72

A beats C by (100 – 72) m = 28 m.

## A runs 1 times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?

Question:
A runs 1 times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?

[A].

200 m

[B].

300 m

[C].

270 m

[D].

160 m

Explanation:

 Ratio of the speeds of A and B = 5 : 1 = 5 : 3. 3

Thus, in race of 5 m, A gains 2 m over B.

2 m are gained by A in a race of 5 m.

 80 m will be gained by A in race of 5 x 80 m = 200 m. 2

Winning post is 200 m away from the starting point.

## 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:

Question:
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:

[A].

60 m

[B].

40 m

[C].

20 m

[D].

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.

## A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:

Question:
A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:

[A].

100 m

[B].

 111 1 m 9

[C].

25 m

[D].

50 m