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 in sec. will they meet at the starting point ?

• A. $1010$ sec
• B. $2772$ sec
• C. $2222$ sec
• D. $1172$ sec

Answer 1

The correct option is B $2772$ sec

Time taken by A to complete a round$=252s$

Time taken by B to complete a round $=308s$

Time taken by C to complete a round $=198s$

LCM of the given numbers will give the time at which they meet at the staring point.

$252=2\times 2\times 3\times 3\times 7$

$308=2\times 2\times 7\times 11$

$198=2\times 9\times 3\times 11$

$LCM=2\times 2\times 3\times 3\times 7\times 11$

$=2772$

Time at which A , B and C meet $=2772seconds$