A and B together can do a piece of work in 13 days and A alone can do it in 18 days. In how many days can B alone do it?

Correct option is D

Given:

A and B together can complete the work in 13 days.

A alone can complete the work in 18 days.

Solution:
Let the time taken by B alone be x days.

According to the given information:

​$$\frac{1}{13} = \frac{1}{18} + \frac{1}{x} \\ \ \\\frac{1}{x} = \frac{1}{13} - \frac{1}{18} \\ \ \\\frac{1}{x} = \frac{18 - 13}{234} \\ \ \\\frac{1}{x} = \frac{5}{234} \\ \ \\x = \frac{234}5=46\frac{4}{5} \text{days}$$​​

So, B alone can complete the work in $$46\frac{4}{5} \text{days}$$​.

Alternate Method :

Assume, Total work = 234 unit [lcm of 13 & 18]

Efficiency of A + B = 18

Efficiency of A = 13

Efficiency of B = 18 -13 =5

Time taken by B = $$\frac{234}5=46\frac{4}{5} \text{days}$$​​