Question

A man busy a number of pens for Rs 80. If he had bought 4 more pens for the same amount, each pen would have cost him Rs 1 less. How many pens did he buy?

Answer 1

$$\begin{gathered} \begin{array}{l}\\ \text{Let the total number of pens be}x.\end{array} \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}: \\ \frac{80}{x}-\frac{80}{x+4}=1 \\ \Rightarrow \frac{80(x+4)-80x}{x(x+4)}=1 \\ \Rightarrow \frac{80x+320-80x}{x^2+4x}=1 \\ \Rightarrow 320=x^2+4x \\ \Rightarrow x^2+4x-320=0 \\ \Rightarrow x^2+(20-16)x-320=0 \\ \Rightarrow x^2+20x-16x-320=0 \\ \Rightarrow x(x+20)-16(x+20)=0 \\ \Rightarrow (x+20)(x-16)=0 \\ \Rightarrow x=-20\text{or}x=\text{16} \\ \mathrm{T}\text{he total number of pens cannot be negative; therefore, the total number of pens is 16.} \end{gathered}$$