Smith and Ajit can complete a task in 12 days and 18 days, respectively. If they work together on the task for 4 days, then the fraction of the task that will be left is:

Let the task be T

Number of days required for Smith to complete the task = 12 days

$$=$$>  Part of the task completed by Smith in 1 day = $$\frac{T}{12}$$

Number of days required for Ajit to complete the task = 18 days

$$=$$>  Part of the task completed by Ajit in 1 day = $$\frac{T}{18}$$

Part of the task completed by both Smith and Ajit in 1 day = $$\frac{T}{12}+\frac{T}{18}=\frac{3T+2T}{36}=\frac{5T}{36}$$

Part of the task completed by both Smith and Ajit in 4 days = $$4\times\frac{5T}{36}=\frac{20T}{36}$$

$$\therefore\ $$Fraction of the task left = $$\text{T}-\frac{20T}{36}=\frac{36T-20T}{36}=\frac{16T}{36}=\frac{4}{9}\text{T}$$

Hence, the correct answer is Option A