2 men or 3 women can complete a job in 96 days. Then 6 men and 7 women will complete the same job in how many days?

Let work done by 1 man in 1 day = $$m$$ and work done by 1 woman in 1 day = $$w$$

=> Work done by 2 men in 1 day = $$\frac{1}{96}$$

=> $$2m=\frac{1}{96}$$

=> $$m=\frac{1}{192}$$

Similarly, work done by 3 women = $$3w=\frac{1}{96}$$

=> $$w=\frac{1}{288}$$

Thus, work done by 6 men and 7 women in 1 day = $$6m+7w$$

= $$6(\frac{1}{192})+7(\frac{1}{288})$$

= $$\frac{1}{32}+\frac{7}{288}=\frac{9+7}{288}$$

= $$\frac{16}{288}=\frac{1}{18}$$

$$\therefore$$ Time taken by 6 men and 7 women to complete the work = 18 days

=> Ans - (A)