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 the same point. After what time will they again at the starting point ?

• A. $26$ minutes and $18$ seconds
• B. $42$ minutes and $36$ seconds
• C. $45$ minutes
• D. $46$ minutes and $12$ seconds
• E. None of these

Answer 1

Answer: (D)

$46$ minutes and $12$ seconds

$A$ complete his round in $252$ seconds
$B$ completes his round in $308$ seconds
$C$ completes his round in $198$ seconds
They will again at starting together after,
LCM of $252,308$ and $198$
$252=2\times 2\times 3\times 3\times 7$
$308=2\times 2\times 7\times 11$
$198=2\times 3\times 3\times 11$
Required LCM $=2\times 2\times 3\times 3\times 7\times 11=2772$ seconds $=46$ minutes $12$ seconds.