Question

Twelve men and 5 women can complete a work in 2 days whereas 4 men and 3 women can complete the same work in 5 days. In how many days can 8 men complete the work?

पर्याय

• 3

• 4

• 5

• 6

Answer 1

4

Explanation:

Let one man and one woman can complete the same work in x and y days respectively.

Then,

${\displaystyle \frac{12}{\text{x}}+\frac{5}{\text{y}}=\frac{1}{2}}$ ...........(i)

and ${\displaystyle \frac{4}{\text{x}}+\frac{3}{\text{y}}=\frac{1}{5}}$ .............(ii)

From (i) and (ii), we have

${\displaystyle \frac{4}{\text{y}}=\frac{1}{10}}$

⇒ y = 40 days.

then, ${\displaystyle \frac{12}{\text{x}}+\frac{5}{420}=\frac{1}{2}}$,

${\displaystyle \text{x}=\frac{12\times 8}{3}=32}$ days.

∴ 8 men complete whole work in ${\displaystyle \frac{32}{8}}$ = 4 days.