8 men and 12 women finish a job in 4 days. While 6 men and 14 women in 5 days. In how many days will 20 women finish the job?

20

8M + 12W = 4 days,

32M + 48W         ..(1)       (Multiplied by 4 to get it done in 1 day)

6M + 14W = 5 days,

30M + 70W        ..(2)        (Multiplied by 5 to get it done in 1 day)

Now, (1) - (2), we get,

⇒ 2M = 22W

⇒ M : W = 22 : 2 = 11 : 1 (Efficiencies)

Putting efficiency in equation (1), and we get the total work 

⇒ [32 (11) + 48(1)] = 400 units.

⇒ Hence, 20 Women can finish the job in = \(\frac{400}{20(1)}\) = 20 days.