A and B start running along a circular track from the same point at the same time in the same direct...........

Quantitative Aptitiude (CLAT) Time & distance

A and B start running along a circular track from the same point at the same time in the same direction. To cover the whole track A needs 5 seconds less than B. They meet for the first time after 30 seconds. How many times will they meet in a minute if they run in opposite directions?

None of these

Explanation:

Let the speeds of A and B be m meters/s and n meters/s respectively and l meters be the circumference. Then time taken by A and B respectively to complete one round will be l/m and l/n seconds. Thus (l/n – l/m)= 5.

If they meet after 30 s, then l/(m-n)=30 or (m-n)/l=1/30

Let l/m=x and l/n=y. Thus 1/y – 1/x =5 and x-y=1/30

or xy = 1/150. Now (x-y)2= x2+y2-2xy or x2+y2= 13/900

(x+y)2= x2+y2+2xy or x+y= 6 or l/(m+n)= 6 seconds =1/10 minutes.

Thus they will meet 10 times in minute.