Correct Answer - Option 3 : 8

GIVEN:

3 men can complete a piece of work in 2 days, while 3 women can complete it in 4 days and 4 children can complete it in 6 days.

FORMULA USED:

Work = Time × Efficiency

CALCULATION:

Let the efficiencies of a man, a woman and a child be ‘m’, ‘w’ and ‘c’ respectively.

⇒ Total work = 3m × 2 = 3w × 4 = 4c × 6

⇒ 1m = 2w = 4c ----- (1)

Now,

Let 2 woman and 1 child together complete the same work in ‘T’ days.

From (1)

2w + 1c = 2c + 1c = 3c

⇒ 3c × T = 4c × 6

⇒ T = 8

∴ 2 woman and 1 children together can complete it in 8 days.