Question

A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs. 1 less. How many books did he buy?

Answer 1

Let the number of books bought be \(x\). Then,

Cost of \(x\) books \(= Rs. 80 \Rightarrow\) Cost of one book \(=Rs \frac{80}{x}\)

If the number of books bought is \(x+4\), then

Cost of one book \(=Rs \frac{80}{x+4}\)

It is given that the cost of one book is reduced by one rupee.

\(\therefore \frac{80}{x} - \frac{80}{x+4}=1\)

\(\Rightarrow 80 \left(\frac{1}{x} - \frac{1}{x+4} \right) =1\)

\(\Rightarrow 80 \left \{ \frac{x+4-x}{x(x+4)} \right \}=1\)

\(\Rightarrow \frac{320}{x^2 + 4x}=1\)

\(\Rightarrow x^2 + 4x=320\)

\(\Rightarrow x^2 + 4x-320=0\)

\(\Rightarrow x^2 + 20x - 16x - 320 =0\)

\(\Rightarrow x(x+20) - 16(x+20)=0\)

\(\Rightarrow (x+20)(x-16) =0\)

\(\Rightarrow x = -20 ~or,~x=16 \Rightarrow x=16\) [\(\because x\) cannot be negative]

Hence, the number of books is 16