Question

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

Answer 1

Step 1: Finding the cost of each book

Let a shopkeeper buys a $\text{'}x\text{'}$ number of books for $\mathrm{Rs}.80$.
Cost of each book $=\frac{80}{x}$
If he bought $4$ more books that is $\left(x+4\right)$ for the same amount
then cost of each book $=\frac{80}{x+4}$

Step 2: Finding the number of books he bought

each book would have cost $\mathrm{Rs}.1$ less, then we get
$$\begin{gathered} \Rightarrow \frac{80}{x}-\frac{80}{x+4}=1 \\ \Rightarrow \frac{80x+320-80x}{x(x+4)}=1 \\ \Rightarrow x^2+4x-320=0 \\ \Rightarrow x^2+(20-16)x-320=0 \\ \Rightarrow x^2+20x-16x-320=0 \\ \Rightarrow x(x+20)-16(x+20)=0 \\ \Rightarrow (x-16)(x+20)=0 \\ \Rightarrow x=16,-20 \end{gathered}$$
Number of books cannot be negative

Therefore number of books shopkeeper buy is $16$