Question

At what time between 4 and 5 will the hands of a clock be at right angles?
1. \(38\dfrac{3}{11}\) minutes past 4
2. \(38\dfrac{9}{13}\) minutes past 4
3. \(38\dfrac{2}{11}\) minutes past 4
4. \(38\dfrac{5}{13}\) minutes past 4

Answer 1

Correct Answer - Option 3 : \(38\dfrac{2}{11}\) minutes past 4

We know, when 2 hands are at right angles, they are 15 minutes space apart and between 4 and 5 o' clock the hands of the clock will be at right angles once. When the minutes hand is 15 minute space ahead of the hour hand.

For this, the minute hand will have to gain  = 20 + 15 = 35 minutes.

As, 55 minutes space is gained in 60 minutes

So, 35 minutes space will be gained in \(\dfrac{60}{55}\)×35 = \(38\dfrac{2}{11}\) minutes.

So, they will be at right angles at \(38\dfrac{2}{11}\) minutes past 4.

Hence, option 3 is the correct answer.