Prasid and Deep separately can do a certain work in 32 and 24 days respectively. They decided to do the work together and Niloy also joined them. If all of them together can complete the same work in 8 days, then how long does Niloy take to do the work alone?

Prasid and Deep separately can do a certain work in 32 and 24 days respectively.

They decided to do the work together and Niloy also joined them. Let Niloy does the same work in x days

If all of them together can complete the same work in 8 days,

According to question,

$$\frac{1}{32} +\frac{1}{24} +\frac{1}{x} =\frac{1}{8}$$

$$\frac{3x + 4x + 96}{96x} =\frac{1}{8}$$

$$5x = 96$$

$$x =\frac{96}{5} $$

Option B is correct.