45 men or 60 boys can do a piece of work in 20 days. How many days will 15 men and 20 boys take to complete the work?

Let work done by 1 man in 1 day = $$m$$ and work done by 1 boy in 1 day = $$b$$

=> Work done by 45 men in 1 day = $$\frac{1}{20}$$

=> $$45m=\frac{1}{20}$$

=> $$m=\frac{1}{900}$$

Similarly, work done by 60 boys = $$60b=\frac{1}{20}$$

=> $$b=\frac{1}{1200}$$

Thus, work done by 15 men and 20 boys in 1 day = $$15m+20b$$

= $$15(\frac{1}{900})+20(\frac{1}{1200})$$

= $$\frac{1}{60}+\frac{1}{60}=\frac{2}{60}=\frac{1}{30}$$

$$\therefore$$ Time taken by 15 men and 20 boys to complete the work = 30 days

=> Ans - (C)