Question

A circular field has a circumference of $360$ km. Two cyclists Sumeet and Samrat start together and can cycle at speeds of $12$ km/hr and $15$ km/hr respectively around the circular field. After how many hours will they meet again at the starting point?

• A. $60$
• B. $8$
• C. $100$
• D. $120$

Answer 1

Answer: (D)

$120$

Time taken by Sumeet to complete one round is $=\frac{360}{12}=30$ hrs

Time taken by Samrat to complete one round is $=\frac{360}{15}=24$ hrs

Time at which they meet again is LCM of $24$ and $30$

$24=2^3\times 3$

$30=2\times 3\times 5$

LCM$(24,30)=120$ hrs