Question

Kumbhakarna starts sleeping between 1 pm and 2 pm and he wakes up when his watch shows such a time that the two hands (i.e., hour-hand and minute-hand) interchange the respective places. He wakes up between 2 pm and 3 pm on the same night. How long does he sleep ?

• A. $55\frac{5}{13}min$
• B. $110\frac{10}{13}min$
• C. $54\frac{6}{13}min$
• D. None of these

Answer 1

The correct option is A $55\frac{5}{13}min$

He starts sleeping between 1 pm and 2 pm and he wakes up between 2 pm and 3 pm such that the two hands interchange the respective places.

It means, when he slept the hour-hand was between 1 and 2 and minute-hand was between 2 and 3.

And when he wakes up the hour-hand was between 2 and 3 and minute-hand was between 1 and 2.

Thus he slept between 1:10 -1:15 and wakes up between 2:05-2:20.

If he sleeps at 1:10 then he should wake up 2:05-2:10 since, the two hands are interchanged.

So, the time he sleeps will be around 55 minutes and not less than 55.

Thus, the time he sleeps is $55+\frac{5}{13}$ minutes.

Hence, option 'A' is correct.