Anil is twice as efficient as Balu, and together, they can complete a task in 12 days. In how many days can Anil alone complete the task?

Correct option is B

Given:

Anil is twice as efficient as Balu.

Together, Anil and Balu can complete the task in 12 days.

Concept Used:

Rate of work =$$\frac{1}{\text{time taken}}$$​​

Solution:

Let the time taken by Balu to complete the task be $$T_B$$​= x. Then, Anil's time taken is $$T_A = \frac{x}{2}$$​ since Anil is twice as efficient as Balu.

The combined rate of Anil and Balu is:

​$$\frac{1}{T_A} + \frac{1}{T_B} = \frac{1}{12}$$​​

​$$\frac{2}{x} + \frac{1}{x} = \frac{1}{12}$$​

​$$\frac{3}{x} = \frac{1}{12}$$​

x = 36

So, Balu takes 36 days to complete the task, and Anil, being twice as efficient, takes:

​$$T_A = \frac{36}{2} = 18 \text{ days}$$​

Thus, Anil can complete the task in 18 days.

Alternate Method:

Efficiency $$\propto$$ $$\frac1{\text{Time}}$$ 

Total Work = (2 + 1)$$\times 12= 3\times 12= 36$$ days 

Anil complete the work = $$\frac{36}{2}=18$$ days​