A can do a piece of work in 12 days, B can do the same work in 15 days. C can do the same work in 9 days. The time taken by them to finish the same work if they work together is:

Correct option is D

Given

A completes the work in 12 days.

B completes the work in 15 days.

C completes the work in 9 days.

Formula Used:

$$\text{Efficiency} = \frac{\text{Total Work}}{\text{Time Taken}}\\ \ \\ \text{Time Required} = \frac{\text{Total Work}}{\text{Total Efficiency}}$$

Solution:

$$\text{Total work =180 units (LCM of 12, 15, and 9).}$$​

$$\text{A's efficiency} = \frac{180}{12} = 15 \text{ units/day}\\ \ \\\text{B's efficiency} = \frac{180}{15} = 12 \text{ units/day}\\ \ \\\text{C's efficiency} = \frac{180}{9} = 20 \text{ units/day}\\ \ \\\text{Total Efficiency} = 15 + 12 + 20 = 47 \text{ units/day}\\ \ \\\text{Time Required} = \frac{180}{47}= 3 \frac{39}{47} \text{days}$$

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