Three persons begin to walk around a circular track The first completes revolution in 151 6 seconds the second in 161 4 econds and the third in 182 3 seconds respectively After what time will they be together at the starting point again?

Three persons begin to walk around a circular track The first com…

MCQ

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

A
$1\ hr \ 40\min$
✓
$1\ hr\ 40\sec$
C
$1.4\ hrs$
D
$1\ hr\ 3\min\ 40\sec$

✓

Answer

Correct option: B.

$1\ hr\ 40\sec$

The time after which all the three will be together will be $LCM$ of
$15\frac{1}{6}, 16\frac{1}{4}, 18\frac{2}{3}$
$LCM$ of $\frac{91}{6}, \frac{65}{4}, \frac{56}{3}=\frac{\text{LCM of 91,65,56}}{\text{HCF of 6,4,3}}=3640$ second $=1$ hour $40$ minits