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)

$7 : 48$

Answer 2

When the clock reads $7'O$ 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 $210^{\circ}+\frac{x}{60}\times30^{\circ}-6x^{\circ}=\pm 54^{\circ}$ 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 $7 : 48$.