A job can be done by 3 skilled workmen in 20 days or by 5 boys in 30 days. How many days will they take if they work together ?

Answer: Option D

$$\begin{array}{rl}& \text{3 men’s 1 day’s work}=\frac{1}{20}\\ & \text{5 boy’s 1 day’s work}=\frac{1}{30}\\ & \left(\text{3 men}+\text{5 boy}\right)\text{’s 1 day’s work}\\ & =\left(\frac{1}{20}+\frac{1}{30}\right)\\ & =\frac{5}{60}\\ & =\frac{1}{12}\end{array}$$
∴ 3 men and 5 boys will complete the work in 12 days.