From 2pm to 3.45pm the time elapsed was 1 hr 45 min or 105 min.

There are only 4 vacancies to be filled for the game and at any time, all 4 are always filled.


The boys would have spent 105 mins for each vacancy so for 4 vacancies,

105 min × 4 = 420 min

A total of 420 min worth of badminton was played but in reality only 105 minutes have passed.


Since there are 5 boys, number of minutes each played when divided equally

= 420 min ÷ 5
= 84 min

(Or 1hr 24 min)

The way they take turns is irrelevant for this question.

Here's an example of how they could take turns :


Boys 1 2 3 4 (21 min)
Boys 2 3 4 5 (21 min)
Boys 1 3 4 5 (21 min)
Boys 1 2 4 5 (21 min)
Boys 1 2 3 5 (21 min)

We have split the 105 min into five sessions of 21 min. The boys play for 21 min for each session.

But each boy only plays 4 sessions in total and sits out for 1 session.

So they only play 21 × 4 = 84 min each