Question

At what time between $2$ and $3$ O' clock the hands of a clock will make an angle of ${160}^{\circ }$ ?

• A. $20$ minutes past $2$
• B. $30$ minutes past $2$
• C. $40$ minutes past $2$
• D. $50$ minutes past $2$

Answer 1

Answer: (C)

$40$ minutes past $2$

If the time is $2$ hours and $x$ minutes after $2$, when the two hands of the clock are same, then the angle formed by minute hand is: $\frac{x}{60}\times 360=6x$
The hour hand moves $\frac{1}{2}$ degree each minute, then angle traced by hour hand is = $60+\frac{x}{2}$
Hence, $6x-(60+\frac{x}{2})=160$
$220=\frac{11x}{2}$
$x=40$
Thus, the angle between them is ${160}^{\circ }$ at a time $40$ minutes past $2$