Question

At what time between $5$ O'clock & $5:30$ will the hands of a clock be at right angle?

• A. $10\frac{10}{11}$ minutes past $5$.
• B. $11\frac{5}{11}$ minutes past $5$.
• C. $9\frac{10}{11}$ minutes past $5$.
• D. $10\frac{9}{11}$ minutes past $5$.

Answer 1

The correct option is A $10\frac{10}{11}$ minutes past $5$.

If the time is $5$ hours and $x$ minutes after $5$, 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 = $150+\frac{x}{2}$
Hence, $150+\frac{x}{2}-6x=90$
$60=\frac{11x}{2}$
$x=\frac{120}{11}$
$x=10\frac{10}{11}$ min. past $5$