Question : 16 boys or 12 women can do a piece of work in 28 days. In how many days will the same work be done by 4 boys and 4 women, if they all work together?
Option 1: 36 days
Option 2: 48 days
Option 3: 44 days
Option 4: 40 days
Correct Answer: 48 days
Solution :
Let the total work to be done is 1 unit.
16 boys or 12 women can do the work in = 28 days
1 boy's 1 day's of work = $\frac{1}{(16 \times 28)} = \frac{1}{448}$
And, 1 woman's 1 day's work = $\frac{1}{(12 \times 28)} = \frac{1}{336}$
The work done by 4 boys and 4 women in one day
= $4 \times (\frac{1}{448}) + 4 \times (\frac{1}{336})$
=$\frac{1}{112}+\frac{1}{84}$
= $\frac{1}{48}$
$\therefore$ The required number of days for 4 boys and 4 women to complete the work together is 48 days.
Hence, the correct answer is 48 days.
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