Question

Aman and Ali together can finish a piece of work in 12 days. If Aman alone can finish the same work in 18 days, then Ali alone can complete the same work in how many days?

• A. 40 days
• B. 32 days
• C. 36 days
• D. 24 days

Answer 1

The correct option is C 36 days

Let Ali take $x$ days to complete the work alone.

$\therefore$ Work done in one day = $\frac{1}{x}$

Work done by Aman in one day = $\frac{1}{18}$

$\therefore$ If they both work together, they can finish $\frac{1}{x}+\frac{1}{18}$ amount of work in one day.

According to question:

$\Rightarrow \frac{1}{x}+\frac{1}{18}=\frac{1}{12}\Rightarrow \frac{1}{x}=\frac{1}{12}-\frac{1}{18}\Rightarrow \frac{1}{x}=\frac{18-12}{12\times 18}\Rightarrow \frac{1}{x}=\frac{6}{216}\Rightarrow \frac{1}{x}=\frac{1}{36}\Rightarrow x=36$

$\therefore$ Ali can complete the same work in 36 days.