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)

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
$=60^{\circ }-{\left(7\frac{1}{2}\right)}^{\circ }={\left(52\frac{1}{2}\right)}^{\circ }$