2 women and 3 men can do a piece of work in 10 days while 3 women and 2 men can do the same work in 8 days. In how many days can 2 women and 1 man do the work?

$12\frac{1}{2}$days

2 w + 3 m ⇒ 10 days

⇒  20 w + 30 m ⇒ 1 day........(i)

3 w + 2 m = 8 days

⇒ 24 w + 16 m = 1 day  ..........(ii)

(i) = (ii)

⇒  20 w + 30 m = 24 w + 16 m

⇒ 14 m = 4 w

⇒ 7 m = 2 w

Efficiency ⇒  m : w = 2 : 7

Now, Total work = Efficiency × Time

From (i)

Total efficiency = 20w + 30m = (20 × 7) + (30 × 2) = 140 + 60 = 200

Total work = 200 × 1 = 200

200 work is to be done by 2 women and 1 man. So,

Efficiency of 2 women and 1 man = (2 × 7) + (1 × 2) = 16

Time = \(\frac{200}{16}\) = 12 \(\frac{1}{2}\)