Question

At 2.15 O’clock the hour and minute hands of the clock from an angle of:
A. $30^\circ $
B. $7\dfrac{1}{2}^\circ $
C. $22\dfrac{1}{2}^\circ $
D. $5^\circ $

Answer 1

Hint: The question is related to the clock. You must know that an hour is equal to $60$ minutes. And on the clock, $1$ to $12$ numbers are mentioned. A clock is a device used to measures, keep, and indicate time. First, find the angle made by the hour hand and minute hand.

Complete step by step answer:
First, we have to check the position of the hour and minute hand for finding the angle made between them.

At 2.15 O’clock the hour hand is between $2$ and $3$ while the minute hand is exactly on $3$.
The angle between the two hands would depend on the angle turned by the hour hand.
An hour hand covers $30^\circ $ in 60 minutes.
The angle between an hour and minute hands of a clock at 2.15 O’clock is,
$=30^\circ - \dfrac{1}{4}(30^\circ )$
Simplifying the above equation,
$ = 30^\circ - 7\dfrac{1}{2}^\circ $
On further simplification
$ = 22\dfrac{1}{2}^\circ $
Therefore, the angle between an hour and minute hands of a clock at 2.15 O’clock is
$ = 22\dfrac{1}{2}^\circ $.

Hence, option C is the correct option.


Note:
Here in this type of question students mostly get confused between the angle made by an hour hand and the minute's hands. Do the calculation part correctly. You can solve this question by an alternative method.
An hour hand covers $30^\circ $ in 60 minutes and so similarly, it would cover $7.5^\circ $in 15 minutes.
Thus, the angle between the hour and minute hands becomes $30^\circ - 7.5^\circ = 22.5^\circ $.

Hence the option C is the correct option for all.