Question

A boy is walking with a constant speed around a circular park. Initially the angle between the line joining his position to the centre and one of the radius of the park is ${30}^{\circ }$. After two minutes the angle between the line joining his position to the centre and the the same radius of the park is once again ${30}^{\circ }$. Find the total time that the boy takes to complete one round.

• A. 12 minutes.
• B. 6 minutes
• C. 24 minutes
• D. 8 minutes

Answer 1

The correct option is A

12 minutes.

Initially the boy subtends an angle of ${30}^{\circ }$ w.r.t the fixed radius at the centre as shown.

After 2 minutes when he subtends an angle of ${30}^{\circ }$ again, then in total he has moved ${60}^{\circ }$ around the park.

Now, total angle to be covered to complete one round is ${360}^{\circ }$.

Therefore, time taken to complete one round = 2 minutes $\times$ $\frac{{360}^{\circ }}{{60}^{\circ }}$ = 12 minutes.