Five men can complete a work in 20 days. Ten women can complete the same work in 15 days. Two men and six women started working together. After 5 days, three women left the work and a new man joined the work. The group continued working together till the end of the work. In how many days will they be able to do the remaining work?

14

As given,

⇒ 5M x 20 = 10W x 15 where, M = Men , W = Women.

⇒ 2M = 3W

⇒ M : W = 3 : 2  (Efficiency)

⇒ Total work =  5M x 20 = 5(3) x 20 = 300 units.    ..(Efficiency × Days = Total work)

Now, (2M + 6W) x 5 = (6 + 12) x 5 = 90 units.

⇒ Remaining work = 300 - 90 = 210 units.

⇒ Now, One  more man joined and 3 women left = 3(3) + 3(2) = 15  (Efficiency)

⇒ Now this group will complete remaining work in = \(\frac{210}{15}\) = 14 days.