4 men can do a piece of work in 6 days while 3 women can complete the same work in 16 days. In how many days 1 man & 2 women together can complete the work?

12

Total Work = m × d

Efficiency of 1 man = m

Efficiency of 1 woman = w

ATQ,

⇒ 4 m × 6 = 3 w × 16 =

\(\frac{m}{w}\) = \(\frac{3 × 16 }{4 × 6}\)

\(\frac{m}{w}\) = \(\frac{2}{1}\)

Therefore,

Total work = 4m × 6

               = 4 × 2 × 6

               = 48

Total efficiency of 1 men and 2 women = 2 + 2 = 4

Time taken by ( 1m +2w) ⇒ \(\frac{48}{1m + 2w}\) ⇒ \(\frac{48}{4}\) ⇒ 12