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1. To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

A. 30 days

B. 35 days

C. 40 days

D. 45 days

Solution:

\begin{aligned} We have \\ B = \frac{3}{2} \times A \\ \to A = \frac{2}{3} \times B \\ One day's work, \\ \Rightarrow A + B = \frac{1}{18} \\ \Rightarrow \frac{2}{3} \times B + B = \frac{1}{18} \\ \Rightarrow \frac{5}{3} \times B = \frac{1}{18} \\ One day's work of B \\ = \frac{3}{90} \end{aligned}

B alone can complete the work in

\begin{aligned} = \frac{90}{3} \\ = 30 days \end{aligned}

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