A class starts at 11 : 00 am and lasts till 2 : 27 pm. Four periods of equal duration are held during this interval. After every period, a rest of 5 minutes is given to the students. The exact duration of each period is:

The correct option is 48 minutes.

Let us break down the solution step-by-step to understand how we arrive at this duration.

Step 1: Calculate the total time interval of the class
The class starts at 11:00 am and ends at 2:27 pm.
From 11:00 am to 2:00 pm is exactly 3 hours, and from 2:00 pm to 2:27 pm is 27 minutes.
Therefore, the total duration is 3 hours and 27 minutes.

To convert this entire duration into minutes:
$\text{Total Time}=(3\times 60)+27=180+27=207\text{minutes}$

Step 2: Determine the total rest time
There are 4 periods of equal duration. Rest intervals of 5 minutes are given only between consecutive periods (i.e., after the first, second, and third periods). No rest is required after the fourth period as the class ends at 2:27 pm.
So, there are 3 rest intervals in total.

$\text{Total Rest Time}=3\times 5=15\text{minutes}$

Step 3: Calculate the total duration spent on actual periods
Subtract the total rest time from the total time interval:
$\text{Time for Periods}=207-15=192\text{minutes}$

Step 4: Find the duration of each period
Since the 192 minutes are divided equally among 4 periods, we divide the remaining time by 4:
$\text{Duration of each period}=\frac{192}{4}=48\text{minutes}$

Thus, the exact duration of each period is 48 minutes.