A and B walk around a circular path of 10 km in circumference, starting together from the same point in the same direction. If their speeds are 3 km/h and 2 km/h respectively, after how many hours will they be again at the starting point?

Correct option is C

Given:
Circumference of the circular path = 10 km
Speed of A = 3 km/h
Speed of B = 2 km/h
Both start together from the same point in the same direction.
Formula Used:
Time taken to complete one full round = $$\frac{\text{Circumference }}{\text{ Speed}}$$​​
Solution:

$$\text{Time}_A = \frac{\text{Circumference}}{\text{Speed}_A} = \frac{10}{3} \text{ hours}$$

​$$\text{Time}_B = \frac{\text{Circumference}}{\text{Speed}_B} = \frac{10}{2} = 5 \text{ hours}$$

​$$\text{Time}_A = \frac{10}{3} \text{ hours}, \quad \text{Time}_B = 5 = \frac{15}{3} \text{ hours}$$​​

LCM of $$\frac{10}{3}$$​ and $$\frac{15}{3}$$​ is $$\frac{\text{LCM}(10, 15)}{3} = \frac{30}{3} = 10$$​ hours.
They will both be at the starting point together after 10 hours.