Question

A class starts at 10 a.m. and lasts till 1.27 p.m. Four periods are held during this interval. After each period, 5 minutes are given free to the students. The exact duration of each period is:-
A. 42 minutes
B. 48 minutes
C. 51 minutes
D. 53 minutes

Answer 1

Hint: For the solution of this question, we will have to follow the below given steps.
We shall assume that the exact duration of one period is ‘x’.
We shall find the total time elapsed between 10 a.m. and 1:27 p.m.
We know that 5 minutes are given free to the students. So, as there have been 4 periods held, hence there would be 3 free breaks given.

Complete step-by-step answer:
We shall form an equation. It is given as follows:-
\[4x\ \ +\ \ 5\ \ \times \ \ 3\ \ =\ \ Total\ \ time\ \ elapsed\]

Total time lapse between 10 a.m. and 1.27 p.m. = 3 hours and 27 minutes
= 3 \[\times \] 60 and 27 minutes
= 180 minutes + 27 minutes
= 207 minutes

Duration of each period =
According to the question, the students are given 5 minutes after each period. As there are 4 periods held, therefore, the number of free breaks given would be 3.
Let us now solve this question.
\[\begin{align}
  & \\
 & 4x\ \ +\ \ 5\ \ \times \ \ 3\ \ =\ \ 207 \\
 & 4x\ \ +\ \ 15\ \ =\ \ 207 \\
 & 4x\ \ =\ \ 207\ \ -\ \ 15 \\
 & 4x\ \ =\ \ 192 \\
 & x\ \ =\ \ \dfrac{192}{4} \\
 & x\ \ =\ \ 48 \\
\end{align}\]

So, the answer to this question is 48 minutes.
This means that the duration of each period is 48 minutes.
Hence, the correct option for this question is (b) 48 minutes.

Note: One needs to form an equation to solve this question. It will make the calculations easier and shorter. If an equation is not formed, then the calculations will be lengthy and time consuming. Also, the calculations must be done carefully as any mistake in the calculus can affect the answer.