# In a one km race, A gives B a start of 100 m and in a one km race, B g

A. 72m

B. 64m

C. 108 m

D. 172 m

### Right Answer is: A

#### SOLUTION

Ratio of speeds of A : B = 1000 : 900 = 100 : 90

Ratio of speeds of B : C = 1000 : 920 = 100 : 92

Therefore, when A moves 1000 m, B moves 900 m and when B moves 900 m, C moves 828 m.

Thus,

Since, C moves 8% less than B in the same time. Thus, C is the worst performer and B is the second worst performer. B will win by him by 72 m.

(i) When it is said that A can give B a start of x metre in y metre race, then it means in y metre race B runs x metre less than A in the same time

NOTE : There is a great difference between ‘can’ and ‘gives’

(ii) When A beats B by t seconds in a race of y metre then it means B is the loser and A is the winner and when A reaches the finishing line B is still some distance back to A. Thus B takes t seconds to cover the remaining distance. Hence, we can calculate the speed of loser (B)

(iii) Through out the race there is always a certain relationship among runners i.e., they always maintain the ratio of speeds. I think this is the nub of all the problems pertaining to the races. Go ahead…

In a one km race, A gives B a start of 100 m and in a one km race, B g