Question

If the list price of a book is reduced by $\mathrm{Rs}5$ a person can buy $5$ more books for $\mathrm{Rs}300$ Then the original cost of the book is?

Answer 1

Step 1: Define a variable and form equation using given conditions

Let the original list price of the book be $\mathrm{Rs}\mathrm{x}$.

Total number of books purchased in $\mathrm{Rs}300=\frac{300}{\mathrm{x}}$

If the price of the book is reduced by $5$

Then the total number of books purchased in $\mathrm{Rs}300=\frac{300}{\mathrm{x}-5}$

Given, Total number of new books $-$Total number of old books $=5$

$\Rightarrow \frac{300}{\mathrm{x}-5}-\frac{300}{\mathrm{x}}=5$

Step 2: Solve the equation obtained

$$\begin{gathered} Wehave,\frac{300}{\mathrm{x}-5}-\frac{300}{\mathrm{x}}=5 \\ \Rightarrow \frac{300\mathrm{x}-300(\mathrm{x}-5)}{\mathrm{x}(\mathrm{x}-5)}=5 \\ \Rightarrow 300\mathrm{x}-300\mathrm{x}+1500=5\mathrm{x}(\mathrm{x}-5) \\ \Rightarrow 1500=5{\mathrm{x}}^2-25\mathrm{x} \\ \Rightarrow 5{\mathrm{x}}^2-25\mathrm{x}-1500=0 \\ \Rightarrow 5\left({\mathrm{x}}^2-5\mathrm{x}-300\right)=0 \\ \Rightarrow \left({\mathrm{x}}^2-5\mathrm{x}-300\right)=0\mathbf{}\mathbf{}[\mathrm{Factorize}\mathrm{quadratic}\mathrm{equation}] \\ \Rightarrow {\mathrm{x}}^2-20\mathrm{x}+15\mathrm{x}-300=0 \\ \Rightarrow \mathrm{x}\left(\mathrm{x}-20\right)+15\left(\mathrm{x}-20\right)=0 \\ \Rightarrow (\mathrm{x}-20)(\mathrm{x}+15)=0 \\ \Rightarrow \mathrm{x}=20,\mathrm{x}=-15 \end{gathered}$$

Therefore, the original price of the book is $20$.