A and B can finish a work in 9 days, B and C can finish it in 12 days and A and C can finish it in 18 days. In how many days can A, B and C finish the work together?

Correct option is A

Given:
A and B together can finish a work in 9 days.
B and C together can finish the same work in 12 days.
A and C together can finish the work in 18 days.
Solution:

Work Rate
A + B =$$\frac{1}{9}$$​​

B + C = $$\frac{1}{12}$$​

A + C = $$\frac{1}{18}$$​​

(A + B) + (B + C) + (A + C) =$$\frac{1}{9} + \frac{1}{12} + \frac{1}{18}$$​

2A + 2B + 2C = $$\frac{4}{36} + \frac{3}{36} + \frac{2}{36}$$

2(A + B + C) $$= \frac{9}{36} = \frac{1}{4}$$​​
A + B + C =$$\frac{1}{8}$$​​
Time taken by A + B + C  to complete the work:
Time = $$\frac{1}{\text{Work Rate}} = \frac{1}{\frac{1}{8}} = 8 \text{ days}$$​​
Alternate Method :​​

Total work = 36 unit.
Efficiency
2(A + B + C) = 4 + 3 + 2 = 9 
A + B + C = 4.5 units/day
Time taken by A + B + C :
​$$=\frac{36}{4.5} = 8 \text{ days}$$​