Question

Find the time between 8 and 9 o'clock when the hands of clock be in the same straight line but not together.

• A. $10\frac{9}{11}$ min. past 8
• B. $10\frac{10}{11}$ min. past 8
• C. $11\frac{10}{11}$ min. past 8
• D. none of these

Answer 1

The correct option is B $10\frac{10}{11}$ min. past 8

If the time is 8 hours and $x$ minutes after 8, 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 = $240+\frac{x}{2}$
Hence, $240+\frac{x}{2}-6x=180$
$60=\frac{11x}{2}$
$x=\frac{120}{11}$
$x=10\frac{10}{11}$ min. past 8