Question

If the angle between the hands of a clock be $54^{\circ }$ and the time it reads between $7$ and $8$, find the time indicated by the clock.

• A. $7:48$
• B. $7:30$
• C. $7:25$
• D. $7:40$

Answer 1

Answer: (A)

When the clock reads $7^{\prime }O$ clock, the angle between the two hands is $7\times 30^{\circ }=210^{\circ }$. If the required time is $7$ hours $x$ minutes, then we must have
$210^{\circ }+\frac{x}{60}\times 30^{\circ }-6x^{\circ }=\pm 54^{\circ }$
As the hour hand revolves $30^{\circ }$ in one hour and minute hand revolves $360^{\circ }$ in one hour, i.e., $6^{\circ }$ in one minute.
$\therefore 210+\frac{x}{2}-6x\pm 54$
$\Rightarrow -\frac{11x}{2}=-210\pm 54$
$=-264$ or $-156$
$\Rightarrow x=48$ or $x=\frac{312}{11}$
But $\frac{312}{11}$ is not a whole number and clock cannot read this time, therefore, the time shown by the clock is $7:48$.