A,B and C can complete a task in 36 , 54 and 72 days respectively. Together they started the task but A left 8 days before the completion of the task while B left 12 days before the completion. the number of days for which C worked is:

Correct option is A

Given:

A, B, and C can complete a work in 36, 54, and 72 days respectively.

A, B, and C started the task together,

A left 8 days before the completion of the work.

B left 12 days before the completion of the work.

Formula used:

Work = Time × Efficiency

Solution:

The efficiency of A = $$\frac{1}{36}$$​​

The efficiency of B =  $$\frac{1}{54}$$​​

The efficiency of C = $$\frac{1}{72}$$​​

Suppose work is completed in x days.

Work done by A = $$\frac{x-8}{36}$$​​

Work done by B = $$\frac{x-12}{54}$$​​

Work done by C = ​$$\frac{x}{72}$$

Total work done by A, B and C = $$\frac{x-8}{36} + \frac{x-12}{54} +\frac{x}{72}$$​​

​$$\begin{aligned}&\implies \frac{(6x - 48 + 4x - 48 + 3x)}{216} = 1 \\&\implies 13x = 216 + 96 \\&\implies x = \frac{312}{13} = 24 \, \text{days}\end{aligned}$$​​

∴ The number of days for which C worked is 24.  

Alternate Solution:   

If A has worked for 8 more days then work done by A in 8 days = $$6\times 8 = 48$$​​

If B has worked for 12 more days then work done by B in 12 days =$$4 \times 12 = 48$$​​

Total Work done = 216 + 48 + 48 = 312 

Time taken by A, B and C to complete this work = $$\frac{312}{13} = 24$$ days.

Hence, Time taken by C to complete the work in 24 days.