Question

In an analog watch, the minute hand is at 12. The angle between the hour hand and the minute hand is ${150}^{\circ }$. What could be the time?

• A. 5 o'clock only.
• B. 7 o'clock only.
• C. either 5 o'clock or 7 o'clock
• D. either 4 o'clock or 8 o'clock.

Answer 1

The correct option is C

either 5 o'clock or 7 o'clock

Total angle subtended at the centre of the clock is ${360}^{\circ }$

Angle subtended by each hour will be, $\frac{{360}^{\circ }}{12}$ = ${30}^{\circ }$

Now an angle of ${150}^{\circ }$ between the hour hand and the minute hand denotes that there is a difference of $\frac{{150}^{\circ }}{30}$ = 5 hours between them.

The minute hand is at 12, so the hour hand must be either 5 hours ahead of it or 5 hours behind it.

5 hours ahead the time is 5 o'clock and 5 hours behind the time is 7 o'clock. So, both can be the answer.