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?
Answer & explanation
Correct answer: option 4
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 \(\frac{1}{2}\)