2 men can complete a piece of work in 3 days while 3 women can complete it in 4 days and 4 children can do it in 6 days. Find in how many days 1 man, 1 woman and 2 children together can complete the same work.

03

⇒ If 2 men can do the work in = 3 days

then, 1 man can do it in = 3 × 2 = 6 days

⇒ If 3 women can do the work in = 4 days

then, 1 woman can do it in = 4 × 3 = 12 days

⇒ If 4 children can do the work in = 6 days

then, 1 child can do it in = 6 × 4 = 24 days

Now,

Let the total work = 24   (LCM of 6, 12, 24)

Eff. of (1m + 1w + 2c) = 4 + 2 + 2 = 8

Therefore,

(1m + 1w + 2c) can do the work in = \(\frac{24}{8}\) = 3 days