12 men and 9 women can finish the work in 10 days. 4 men and 12 women can finish the same work in 15 days, if 10 men start the work and worked for 6 days and after that 'x' men and 'x+2' women join the work and total work finished in 21 days, find the value of 'x'.

4

(12 M + 9 W) × 10 = (4 M + 12 W) × 15

      120 M + 90 W = 60 M + 180 W

                   60 M = 90 W

                     2 M = 3 W ⇒ \(\frac{M}{W}\) = \(\frac{3}{2}\)

⇒ Total work = (12 × 3 + 9 × 2) × 10 = 540

10 men worked for 6 days, hence work done = 10 × 3 × 6 = 180

Remaining work = 540 - 180 = 360

ATQ, 

[ xM + (x+2) W] × 15 = 360

       3 x + (x + 2) × 2 = 24

                      5x + 4 = 24

                              x = 4