Question

Three persons begin to walk around a circular track. The first completes revolution in $15\frac{1}{6}$ seconds, the second in $16\frac{1}{4}$ seconds and the third in $18\frac{2}{3}$ seconds, respectively. After what time will they be together at the starting point again?

• A. 1 hr 40 min
• B. 1 hr 40 sec
• C. 1.4 hrs
• D. 1 hr 3 min 40 sec

Answer 1

The correct option is B 1 hr 40 sec

The time after which all the three will be together is the L.C.M. of $15\frac{1}{6}$, $16\frac{1}{4}$ and $18\frac{2}{3}$
L.C.M of $\frac{91}{6}$, $\frac{65}{4}$ and $\frac{56}{3}$
$=\frac{LCMof91,65,56}{HCFof6,4,3}$
$=3640seconds=1hr,40sec$.