Question

P, Q and R start at the same time and in the same direction to run around a circular stadium. P completes a round in $252$ seconds, Q in $308$ seconds and R in $198$ seconds, all starting at the same point. After what time will they meet again at the starting point?

• A. $26$ mins $18$ secs
• B. $42$ mins $36$ secs
• C. $46$ mins $12$ secs
• D. $45$ mins

Answer 1

The correct option is C $46$ mins $12$ secs

$A$ 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 $LCM=2\times 2\times 3\times 3\times 7\times 11=2772seconds=46minutes12seconds.$