Question

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

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

Answer 1

Answer: (A)

$10\frac{10}{11}$ minute past $5$

In a minute, the hour hand moves by half degrees and the minute hand moves by six degrees.
The angle at $5$ o'clock between the two hands is $150$ degrees.
For it to make a right angle, it should move $m$ minutes
$150=90+(6m-\frac{m}{2})$
$60=\frac{12m-m}{2}$
$120=11m$
$m=10\frac{10}{11}$
It should be $10\frac{10}{11}$ past $5$ for the two hands to be at right angle.
Answer is Option $A.$