2 men and 7 women can do a piece of work in 14 days whereas 3 men and 8 women can do it in 11 days. In how many days 5 men and 4 women can do the same work?

2 men and 7 women can do a piece of work in 14 days

=> $$2m+7w=\frac{1}{14}$$ ---------------(i) $$\times3$$

Also, $$3m+8w=\frac{1}{11}$$ -------------(ii) $$\times2$$

Solving above equations, we get : $$5w=\frac{3}{14}-\frac{2}{11}$$

=> $$5w=\frac{33-28}{154}$$

=> $$w=\frac{1}{154}$$

Thus, $$2m=\frac{1}{14}-\frac{7}{154}$$

=> $$2m=\frac{22-14}{308}$$

=> $$m=\frac{2}{154}$$

Thus, 5 men and 4 women can do the same work in = $$(5\times\frac{2}{154})+(4\times\frac{1}{154})$$

= $$\frac{14}{154}=\frac{1}{11}$$

$$\therefore$$ Time taken is 11 days

=> Ans - (A)