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 ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{A's 1 day's work}} = \frac{1}{{24}} \cr & {\text{B's 1 day's work}} = \frac{1}{5} \cr & {\text{C's 1 day's work}} = \frac{1}{{12}} \cr & \therefore \left( {{\text{A}} + {\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} \cr & = \frac{1}{{24}} + \frac{1}{5} + \frac{1}{{12}} \cr & {\text{L}}{\text{.C}}{\text{.M of 24, 5 and 12}} \cr} $$

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

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