A and B can do a piece of work in 18 days, B and C can do the same work in 32 days and A and C can do the same in 52 days. The time taken by A, B and C together to do the work is:

Correct option is A

Given:

A + B = 18 days

B + C = 32 days

A + C = 52 days

Formula Used:  ​

Total Work = Efficiency × Time

Solution:

Total work = LCM(18, 32, 52) = 3744 units

Efficiency;

A + B =$$\frac{3744}{18}$$​ = 208 units/day

B + C = $$\frac{3744}{32}$$​= 117 units/day

A + C = $$\frac{3744}{52}$$​ =  72 units/day

Now, 

(A + B) + (B + C) + (A + C) = 2(A + B + C) = 208 + 117 + 72

A + B + C = $$\frac{397}{2}$$​ units/day

Time for all three together = $$\frac{3744}{397/2}$$​​

=$$\frac{3744 \times 2}{397}$$​​

=$$\frac{7488}{397}$$​​

=$$18\frac{342}{397}$$​days