# Races and Games Multiple Choice Questions

## Races and Games

Question 1.

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
Explanation :

A : B = 200 : 169.
A : C = 200 : 182.
C/A = (C/A x A/B) = (182/200 x 200/169) = 182 : 169.
When C covers 182 m, B covers 169 m.
When C covers 350 m, B covers (169/182 x 350) m = 325 m.
Therefore, C beats B by (350 - 325) m = 25 m.

Question 2.

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
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 x 360) m= 480 m.
Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind. A wins by 20 m.

Question 3.

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
Explanation :

When B runs 25 m, A runs 45/2m.
When B runs 1000 m, A runs (45/2 x 1/25 x 1000) m = 900 m. B beats A by 100 m.

Question 4.

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 :

4.14 kmph

Question 5.

In a 300 m race, A beats B by 22.5 m or 6 seconds. B's time over the course is:

 A. 86 sec B. 80 sec C. 76 sec D. None of these
Explanation :

B runs 45/2 m in 6 sec. B covers 300 m in (6 x 2/45 x 300) sec= 80 sec.