Question

$3$ runners had to run in a rectangular ground with perimeter $360km$. They start at the same point. The distance covered by each runner is $48km,60km$ and $72km$ everyday respectively. After how many days will they meet again?

• A. $28$
• B. $30$
• C. $4$
• D. $5$

Answer 1

Answer: (B)

$30$

Perimeter of a rectangular ground $=360km$

The first runner will need $7.5days=\frac{360}{48}$

The second runner will need $6days=\frac{360}{60}$

The third runner will need $5days=\frac{360}{72}$

LCM of $7.5,6$ and $5$ is $30.$
The first runner will make $4$ rounds in $7.5days=\frac{30}{7.5}$

The second runner will make $5$ rounds in $6days=\frac{30}{6}$

The third runner will make $6$ rounds in $5days=\frac{30}{5}$
They will all meet again in $30days$.
Therefore$,$ $B$ is the correct answer.