A, B and C can complete a piece of work in 24, 5 and 12 days respectively. Working together, they will complete the same work in ?

Answer: Option D

$$\begin{array}{rl}& \text{A’s 1 day’s work}=\frac{1}{24}\\ & \text{B’s 1 day’s work}=\frac{1}{5}\\ & \text{C’s 1 day’s work}=\frac{1}{12}\\ & \therefore \left(\text{A}+\text{B}+\text{C}\right)\text{’s 1 day’s work}\\ & =\frac{1}{24}+\frac{1}{5}+\frac{1}{12}\\ & \text{L}\text{.C}\text{.M of 24, 5 and 12}\end{array}$$

2	24 - 5 - 12
2	12 - 5 - 6
3	6 - 5 - 3
	2 - 5 - 1

$$\begin{array}{rl}& \text{2}\times 2\times 3\times 2\times 5=120\\ & =\frac{5+24+10}{120}\\ & =\frac{39}{120}\\ & =\frac{13}{40}\end{array}$$
Time taken by A, B and C to complete the work, working together
$$\begin{array}{rl}& =\frac{40}{13}\\ & =3\frac{1}{13}\text{days}\end{array}$$