9 men and 12 women can complete a work in 4 days, whereas 3 men and 6 women can complete it in 10 days. The number of days in which 15 women will complete the work is:

Let efficiency of 1 man and 1 woman to complete the work in 1 day be $$m$$ and $$w$$ respectively.

9 men and 12 women can complete a work in 4 days, => $$9m+12w=\frac{1}{4}$$ -----------(i)

Similarly, $$3m+6w=\frac{1}{10}$$ ---------------(ii)

Multiplying equation (ii) by 2 and then subtracting it from equation (i), we get :

=> $$9m-6m=\frac{1}{4}-\frac{1}{5}$$

=> $$m=\frac{1}{60}$$

And $$6w=\frac{1}{10}-\frac{1}{20}$$

=> $$w=\frac{1}{120}$$

$$\therefore$$ Number of days required by 15 women = $$\frac{1}{15w}=\frac{120}{15}=8$$ days

=> Ans - (D)