Races and Games

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

Answer: Option C

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.

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

Answer: Option B

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.

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

Answer: Option B

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

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

Answer: Option B

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.

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

Answer: Option D

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.

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

Answer: Option B

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.

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

Answer: Option C

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.

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

Answer: Option A

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.

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

Answer: Option C

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.

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

Answer: Option A

Explanation:

When B runs 25 m, A runs	45	m.
	2

When B runs 1000 m, A runs		45	x	1	x 1000	m	= 900 m.
		2		25

B beats A by 100 m.