Question

The angle between two hands of a clock at quarter past one is

• A. $60^{\circ}$
• B. $\left(52 \frac{1}{2}\right)^{\circ}$
• C. $\left(\frac{\pi}{3}\right)^{c}$
• D. none of these

Answer 1

Answer: (B)

$\left(52 \frac{1}{2}\right)^{\circ}$

Answer 2

If hours hand were at $1$ and minutes hand at $3$, the angle between the two hands would have been $60^{\circ}$. In $15$ minutes, hours hand revolves through $\left( \frac{360 \times 15}{720} \right)^{\circ} = \left(7 \frac{1}{2} \right)^{\circ}$ ($\because$ In $12$ hours, i.e., $720$ min, hours hand revolves through $360^{\circ}$) $\therefore$ Required angle between the hands of clock $= 60^{\circ} - \left(7 \frac{1}{2}\right)^{\circ} = \left(52 \frac{1}{2}\right)^{\circ}$