16 men and 12 women together complete a work in 20 days. If 18 women complete the same work in 40 days. Then how many days will be taken by 12 men and 27 women together to complete the same work?

∵ In 20 days the work is completed by = 16 men + 12 women
∴ In 1 day the work is completed by = 20 x (16 men + 12 women )
= 320 men + 240 women
In 40 days the work is complete by 18 women
∴ 1 day the work is complete by = 18 x 40 = 720 women
∵ 720 women = 320 men + 240 women
⇒ (720 - 240)women = 320 men
⇒ 480 women = 320 men
∴ 1 men = 480/320 = 3/2 women
∴ 12 men + 27 women = 12 x (3/2) + 27 = 45 women
∵ 18 women complete work in 40 days
∴ 45 women complete 1 work = 40 x 18/45 = 16 days