Question

A circular field has a circumference of $360$ km. Three cyclist start together and can cycle $48,60$ and $72$ km a day, round the field. When will they meet again?

• A. $7$ days
• B. $15$ days
• C. $23$ days
• D. $30$ days

Answer 1

The correct option is D $30$ days

Circumference of field $=360km$

Cyclist $1$ can cover $48km$ in $1$ day

$\therefore$ For covering $360km=\frac{360}{48}=7.5$ days

Cyclist $2$ can cover $60km$ in $1$ day

$\therefore$ for covering $360km=\frac{360}{60}=6$ days

Cyclist $3$ can cover $72km$ in $1$ day

$\therefore$ for covering $360km=\frac{360}{72}=5$ days

$7.5$ days = $7.5\times 24=180$ hours

$6$ days = $6\times 24=144$ hours

$5$ days = $5\times 24=120$ hours

$LCM$ of $180,144$ & $120$ is $720$

Now = $\frac{720}{24}=30$ days

$\therefore$ The cyclist will meet after $30$ days