Question

Rajan starts sleeping between 2 pm and 3 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 3 pm and 4 pm on the same day. How long does he sleep ?
(1) 55 5/13 minutes
(2) 54 6/13 minutes
(3) 110 10/13 minutes
(4) None of these

Answer 1

Given: Time slept = 2pm - 3pm

Time to wake up - 3pm - 4pm

To Find: Duration of the sleep

Solution:

Time at which Rajan starts sleeping = 1 pm and 2 pm

Time at which Rajan wakes up = 2 pm and 3 pm

Since, the two hands have interchanged the respective places, thus when he slept the hour-hand was between 1 and 2 and the minute-hand was between 2 and 3.

Now, when he gets up the hour-hand is between 2 and 3 and the minute-between 1 and 2.

Thus, he slept between the time = 1:10 -1:15 and

He woke up between = 2:05-2:20.

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

Answer : The time he slept will be around 55 + 5/13 minutes