Question

A takes 10 days than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.

Answer 1

$$\begin{gathered} \begin{array}{l}\\ \text{Let B takes}x\text{days to complete the work.}\end{array} \\ \mathrm{Therefore},\text{A will take}(x-10)\text{days.} \\ \therefore \frac{1}{x}+\frac{1}{(x-10)}=\frac{1}{12} \\ \Rightarrow \frac{(x-10)+x}{x(x-10)}=\frac{1}{12} \\ \Rightarrow \frac{2x-10}{x^2-10x}=\frac{1}{12} \\ \Rightarrow x^2-10x=12(2x-10) \\ \Rightarrow x^2-10x=24x-120 \\ \Rightarrow x^2-34x+120=0 \\ \Rightarrow x^2-(30+4)x+120=0 \\ \Rightarrow x^2-30x-4x+120=0 \\ \Rightarrow x(x-30)-4(x-30)=0 \\ \Rightarrow (x-30)(x-4)=0 \\ \Rightarrow x=30\text{or}x=\text{4} \\ \mathrm{Number}\mathrm{of}\mathrm{days}\mathrm{to}\mathrm{complete}\mathrm{the}\mathrm{work}\mathrm{by}\text{B cannot be less than that by A; therefore, we get:} \\ x=30 \\ \mathrm{Thus},\text{B completes the work in 30 days}\text{.} \end{gathered}$$