Question

Three persons $A,B$ and $C$ run along a circular path $12$ km long. They start their race along the same point at the same time with a speed of $3$ km/hr, $7$ km/hr and $13$ km/hr respectively. After what time will they meet again?

• A. $16$ hours
• B. $24$ hours
• C. $9$ hours
• D. $12$ hours

Answer 1

The correct option is D $12$ hours

Time taken by $A=\frac{12}{3}$ hours $=4$ hours.

Time taken by $B=\frac{12}{7}$ hours

Time taken by $C=\frac{12}{13}$ hours

$\therefore A,B,C$ will meet again after an interval.

$=$ L.C.M. of $(\frac{4}{1},\frac{12}{7}\text{and}\frac{12}{13})$ hours

$=\frac{\text{L.C.M. of}(4,12,12)}{\text{H.C.F. of}(7,13)}=\frac{12}{1}$ hours

$=12$ hrs