Question

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

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

Answer 1

The correct option is C $40$ minutes past $2$

In a minute, the hour hand moves by half degrees and the minute hand moves by six degrees.
The angle at $2$ o' clock between the two hands is $60$ degrees.
For them to make $160$ degrees between, it should move $m$ minutes
$160=(6m-\frac{m}{2})-60$
$220=\frac{12m-m}{2}$
$440=12m-m$
$11m=440$
$m=40$ minutes

It should be $40$ minutes past $2$ for the two hands to be at $160$ degrees.
Answer is option $C.$