In a 100 m race, A can give B start of 30 m and C start of 37 m. In the same race B can give C start of how many meters?

Question

A and B run a km race. If A gives B a start of 100 m, A wins by 20 sec and if A gives B a start of 50 sec, B wins by 30 m. Then what is the time taken by A to run a km?

Answer 1

Speed of
A - 100/x
B - 70/x
C - 63/x
ie., when A reaches the finish line after x seconds, B will be at the 70 meter point and C at 63.
since distance is proportional to time, we have

distance-------time
70---------------- x
100 --------------?

or time taken for B to reach the finish line = ((100*x)/70)= (10/7)*x ( assuming the speed will remain same throughout).
Now the distance that C covers at the same time will be helpful in determining how much of a head start B can give to C.

distance C covers in (10/7)x seconds is

distance---------- time
63------------------ x
? ------------------ (10/7)x
= (10/7)*x*63/x = 90 meter.
which means after 100 meters B can create a lead of 10 meters with respect to C or B can afford to give C a head start of 10 meter or less to win.

Answer 2

Very simple answer!

If B in 70 meters is 7 m ahead of C, in 100 meters would be 10 m ahead.

Comments

That is a nice way of looking at the problem which I clearly missed. Nice Job ! Even though I understood what you are trying to say here, it is possible that some won't. So a bit more description on your answer would have been better.