Question

Mark (✓) against the correct answer:
A works twice as fast as B. If both of them can together finish a peice of work in 12 hours, then B alone can do it in
(a) 24 hours
(b) 27 hours
(c) 36 hours
(d) 18 hours

Answer 1

(c) 36 hours

$$\begin{gathered} \text{Suppose}\mathrm{B}\mathrm{take}\text{s}\mathrm{x}\mathrm{hour}\text{s to complete the work}. \\ \therefore \mathrm{B}\text{'}\mathrm{s}1\mathrm{hour}\mathrm{work}=\frac{1}{\mathrm{x}} \\ \mathrm{A}\mathrm{works}\mathrm{twice}\mathrm{as}\mathrm{fast}\mathrm{as}\mathrm{B}. \\ \therefore \text{A's}1\mathrm{hour}\mathrm{work}=\frac{2}{\mathrm{x}} \\ \frac{1}{12}=\frac{1}{\mathrm{x}}+\frac{2}{\mathrm{x}}=\frac{3}{\mathrm{x}} \\ \Rightarrow \mathrm{x}=36\mathrm{hours} \end{gathered}$$