Question

4 men and 2 boys can do a job in $6\frac{2}{3}$ days. 3 women and 4 boys can finish the same job in 5 days. Also 2 men and 3 women can finish the same job in 4 days. In how many days can 1 man, 1 woman and 1 boy finish the work at their double efficiency___

Answer 1

In 1 day 4 men and 2 boys can do $\left[\frac{100}{\left(\frac{20}{3}\right)}\right]\%=15\%$ of the job. ... (i)

In 1 day 3 women and 4 boys can do $\frac{100}{5}=20\%$ of the job.... (ii)

In 1 day 2 men and 3 women can do $\frac{100}{4}=25\%$ of the job.... (iii)

So, adding (i), (ii), (iii)

6 men, 6 women and 6 boys can do 15 + 20 + 25 = $60\%$ of the job in 1 day.

So, 1 man, 1 woman and 1 boys can do $10\%$ of the job in a day.

All double their efficiency, they can do $20\%$ of the job in a day.

They can complete the job in $\frac{100}{20}$ = 5 days.