If 12 men or 18 women can do a work in 14 days, then how many days will 8 men and 16 women do the same work?

9

Solution

12M or 18W = 14 days   ....(1)

12M x 14 = 18W x 14  

168M = 252W

6M = 9W

M : W = 9 : 6 = 3 : 2

Now putting ratio in (1)

Total work = 12(3) x 14 = 36 x 14 = 504 units

Time taken by 8M and 16W to complete the total work = \(\frac{504}{8(2)\;+16(2)}\) = \(\frac{504}{56}\) = 9 days,

Therefore, 8M and 16W will complete the total work in 9 days.