Question

A, B and C start at the same time in the same direction to run around a circular stadium A completes a round in 252 seconds B in 308 seconds and C in 198 seconds all starting at the same point After what time will they meet again at the starting point ?

• A. 26 minutes 18 seconds
• B. 42 minutes 36 seconds
• C. 45 minutes
• D. 46 minutes 12 seconds

Answer 1

The correct option is D 46 minutes 12 seconds

Rate of running by $A,B,C=\frac{1}{252}:\frac{1}{308}:\frac{1}{198}$

They will be at staring point at a time which

is a multiple of time taken to funchih one round

Hence they'll must at a there which is LCM $(252,308,198)$

$=LCM(252,308,198)$

$=LCM(2^2{.7}^1{.3}^2,2^2{.7}^1,{11}^1,2^1{.3}^2,{11}^1)$

$=2^2{.3}^2{.7}^1{.11}^1$

$=2772$ seconds

$=A6$ mins $12$ sec