A, B and C can complete a piece of work in 6, 12 and 24 days respectively. They all together will complete the work in:

Correct option is A

Given:

A can complete the work in 6 days

B can complete the work in 12 days

C can complete the work in 24 days

Required: Time taken by A, B, and C together to complete the work

Formula Used:

Work per day $$= \frac{1}{A} + \frac{1}{B} + \frac{1}{C}$$​

Time to complete work =$$\frac{1}{\text{Work per day}}$$​

Solution:

Combined work per day $$= \frac{1}{6} + \frac{1}{12} + \frac{1}{24} = \frac{4 + 2 + 1}{24} = \frac{7}{24}$$​

Time = $$\frac{1}{\frac{7}{24}} = 3\frac{3}{7} \text{ days}$$

Alternate Method:

Required Time = $$\frac{24}{7}=3\frac37$$