A works twice as fast as B. If both of them together can finish a job in 12 days, then how many days will B take to finish the job alone?

Correct option is B

Given:

A works twice as fast as B.

A and B together can finish the job in 12 days.

Formula Used:

$$\text{Work Rate of A and B Together}, \\ = \frac{1}{T_{\text{together}}} = \text{Work Rate of A} + \text{Work Rate of B}$$​

Solution: 

Let T_bbe the time taken by B alone to complete the job.

Then, 

A’s time = $$\frac{T_B}{2}$$ 

Now, 

​ $$\frac{1}{12} = \frac{2}{T_B} + \frac{1}{T_B} = \frac{3}{T_B}$$

$$\frac{1}{12} = \frac{2}{T_B} + \frac{1}{T_B} = \frac{3}{T_B}$$

$$T_B = 3 \times 12 = 36 \, \text{days}$$​​

Thus B will take 36 days to finish the job alone.