3 men or 4 women can complete a job in 120 days. 12 men and 16 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 3 men in 1 day = $$\frac{1}{120}$$

=> $$3m=\frac{1}{120}$$

=> $$m=\frac{1}{360}$$

Similarly, work done by 4 women = $$4w=\frac{1}{120}$$

=> $$w=\frac{1}{480}$$

Thus, work done by 12 men and 16 women in 1 day = $$12m+16w$$

= $$12(\frac{1}{360})+16(\frac{1}{480})$$

= $$\frac{1}{30}+\frac{1}{30}=\frac{2}{30}=\frac{1}{15}$$

$$\therefore$$ Time taken by 12 men and 16 women to complete the work = 15 days

=> Ans - (C)