A and B working together can finish a task in 18 days. B and C working together can finish it in 24 days. A and C working together can finish it in 36 days. In how many days will A, B and C finish the same task, working separately?

Correct option is C

Given:

A and B working together  finish the  task =  18 days.

B and C working together  finish the task  =  24 days

A and C working together  finish the task = 36 days.

Solution:

Total work = LCM of (18 , 24, 36) = 72 unit 

Efficiency of A +  B = $$\frac{72}{18} = 4$$ unit per day   .......... equation{1}

Efficiency of B +  C = $$\frac{72}{24} = 3$$ unit per day  ...........equation{2}

Efficiency of A +  C = $$\frac{72}{36} = 2$$ unit per day  ..........equation{3}

Sum these equation - 

Efficiency of  2(A + B + C) =   9  unit/day 

= 4.5 unit/day 

Efficiency of C = 4.5 - 4 = 0 = 0.5 

Efficiency of A = 4.5 - 3 = 1.5 unit/day 

Efficiency of B = 4.5 -2 = 2.5 unit/day 

C alone complete the work = $$\frac{72}{0.5} = 144 \ days$$

A alone complete the work = $$\frac{72}{1.5} = \frac{144}{3} \ days$$   = 48 days 

B alone complete the work = $$\frac{72}{2.5} = \frac{144}{5} \ days$$  = $$28\frac{4}{5}$$  days​