Question

$A$ does half as much work as $B$ in three fourth of the time. If together they take 18 days to complete a work, how much time shall $B$ take to do it?

• A. $40$ days
• B. $35$ days
• C. $30$ days
• D. $45$ days

Answer 1

Answer: (C)

$30$ days

Let $B$ complete the work in $x$ days.

$\Rightarrow B$'s 1 days' work $=\frac{1}{x}$

$\therefore A$ complete $\frac{1}{2}$ of the work in $\frac{3x}{4}$ days

$\Rightarrow A$'s 1 days' work $=\frac{\frac{1}{2}}{\frac{3x}{4}}=\frac{2}{3x}$

Given, $\frac{1}{x}+\frac{2}{3x}=\frac{1}{18}$

$\Rightarrow \frac{3+2}{3x}=\frac{1}{18}\Rightarrow \frac{5}{3x}=\frac{1}{18}$

$\Rightarrow 3x=90\Rightarrow x=30$