Question

At what time, between four o'clock and five o'clock, will the hands of a clock make an angle of 100${}^o$?

• A. $4$ hours $40$ minutes
• B. $4$ hours $20$ minutes
• C. $4$ hours $10$ minutes
• D. $4$ hours $25$ minutes

Answer 1

The correct option is A $4$ hours $40$ minutes

In 1 hour the hour hand of a clock moves $360÷12=30°$

In one hour the minute arm of the clock moves $360÷60=6°$

In one minute the hour hand moves$30÷60=0.5°$

From 12 o'clock to 4 o'clock will subtend 30×4=120°

And in x minutes, hour hand Will subtend x°/2

Now in x minutes the minute arm will subtend=6x°

So $100°$ will be subtended when the minute hand is after the hour hand.

$6x-[120+(x/2\left)\right]=100°$

$11x/2=220°$

$x=40minutes$

The time would be $4hour+40minutes$ i.e. $4:40$ would be the time when both the arms will be at a $100°$angle.

Option A is the correct answer.