4 men and 10 women were put on a work. They completed ⅓ of the work in 4 days. After this 2 men and 2 women were increased. They completed ²⁄₉ more of the work in 2 days. If the remaining work is to be completed in 3 days, then how many more women must be increased?

Remaining work

4 men + 10 women do 1 work in 12 days.

6 men + 12 women do 1 work in 9 days.

48 men + 120 women = 54 men + 108 women

⇒ 6 men = 12 women

⇒ 1 men = 2 women

∴ In 12 days 1 work requires 9 men

∴ In 1 day 1 work requires 9 × 12 men

∴ In 3 days 1 work requires

men

∴ In 3 days ⁴⁄₉ work requires

men

There are 6 men and 12 women or (12 men equivalent)

So, 4 men equivalent is required additionally

∴ 8 women are needed to finish the work.