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Q:

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) 28m	D) 29m

Answer & Explanation Answer: C) 28m

Explanation:

A : B = 100 : 75

B : C = 100 : 96.

A : C = (A/B*B/C) = (100/75*100/96) = 100/72 =100:72

A beats C by (100 - 72) m = 28 m.

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Q:

A runs $1 \frac{2}{3}$ 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) 300m
C) 270m	D) 160m

Answer & Explanation Answer: A) 200 m

Explanation:

Ratio of the speeds of A and B =5 : 1 = 5 :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 $(\frac{5}{2} * 80)$ m =200m

=> Winning post is 200 m away from the starting point.

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Q:

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

A) 100 m	B) 75 m
C) 25 m	D) 50m

Answer & Explanation Answer: A) 100 m

Explanation:

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

When B runs 1000 m, A runs (45/2*1/25*1000)m = 900 m.

B beats A by 100 m.

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Q:

In a 200 metres race A beats B by 35 m or 7 seconds. A's time over the course is:

A) 40 sec	B) 47sec
C) 33sec	D) none of these

Answer & Explanation Answer: C) 33sec

Explanation:

B runs 35 m in 7 sec.

B covers 200 m in (7/35*200) = 40 sec.

B's time over the course = 40 sec.

A's time over the course (40 - 7) sec = 33 sec.

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Q:

In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:

A) 20m	B) 25m
C) 22.5m	D) 9m

Answer & Explanation Answer: A) 20m

Explanation:

Distance covered by B in 9 sec. = (100/45)*9m = 20m

A beats B by 20 metres.

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Q:

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) 18.5 m

Answer & Explanation Answer: B) 25 m

Explanation:

A : B = 200 : 169.

A : C = 200 : 182.

C/B = (C/A*A/B) = (182/200*200/169) = 182:169

When C covers 182 m, B covers 169 m.

When C covers 350 m, B covers (169/180*350)m = 325 m

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

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Q:

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) 5.4m	B) 4.5m
C) 5m	D) 6m

Answer & Explanation Answer: D) 6m

Explanation:

A : B = 100 : 90.

A : C = 100 : 87.

B/C = (B/A*A/C) = (90/100*100/87) = 30/29

When B runs 30 m, C runs 29 m.

When B runs 180 m, C runs (29/30*180)m =174m

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

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Q:

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) 60m	B) 40m
C) 20m	D) 10m

Answer & Explanation Answer: C) 20m

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 (4/3)*360 = 480 m.

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

A wins by 20 m.

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