Question

At what point of time after 3 o'clock, do the hour-hand and the minute-hand of a clock occur at right angles for the first time?

Answer 1

at 9 o'clock ...option 1 is right

Answer 2

At 3 hours 32  8/11 minutes the hour-hand and the minute-hand of a clock occur at right angles for the first time after  3 o'clock,

At 3 o'clock  , Minute hand is at 12 and Hour hand is at 3

Both are at right angles and Hour  hand is 90° ahead of minute hand

For Every 1° of Hour hand moment Minute hand moves 12°

In 1 minute hour hand moves 0.5°  and Minute hand moves 6°

Now Minute hand should move 180° more than Hour hand to be at 90°

Let say same thing happens after t minutes then:

6t = 0.5t + 180

=> 5.5t = 180

=> t = 360/11

=> t = 32  8/11  minutes

Time in clock will be 3 hours 32  8/11  minutes

Correct option is d) 3 hours 32  8/11  minutes

At 3 hours 32  8/11 minutes the hour-hand and the minute-hand of a clock occur at right angles for the first time after  3 o'clock,