Answer

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**Hint:**We start solving by assuming variables for original list price and total no. of books that can be bought before reducing price. Now we made changes to the variables as given in the problem after reducing the price. We use these two equations to get the total no. of books which can be bought before reducing the price. Using this value, we find the value of original list price of the book.

**Complete step by step answer:**

Given that if the price of the book is reduced by Rs. 5, then we can buy 5 more books for Rs. 300. We need to find the original list price of the book.

Let us the cost price per each book be Rs. X. Let us assume that we can buy ‘y’ books for Rs. 300.

So, We get X.y = 300.

$\Rightarrow X=\dfrac{300}{y}$ ---(1).

We get the list price for 1 book as $\dfrac{300}{y}$.

According to the problem and we are getting 5 extra books for Rs. 300, if the price of the book is reduced by Rs. 5.

So, the new price for each book is Rs. (X – 5) and the total no. of books we can buy for Rs. 300 is (y+5).

So, $\Rightarrow \left( X-5 \right)\times \left( y+5 \right)=Rs.300$.

From equation (1), we have $X=\dfrac{300}{y}$ and we use this result.

$\Rightarrow \left( \dfrac{300}{y}-5 \right)\times \left( y+5 \right)=300$.

$\Rightarrow \left( \dfrac{300}{y}\times y \right)+\left( \dfrac{300}{y}\times 5 \right)-5y-25=300$.

$\Rightarrow 300+\dfrac{1500}{y}-5y-25=300$.

$\Rightarrow \dfrac{1500}{y}-5y=300-300+25$.

$\Rightarrow \dfrac{1500-5{{y}^{2}}}{y}=25$.

$\Rightarrow 1500-5{{y}^{2}}=25y$.

$\Rightarrow 5{{y}^{2}}+25y-1500=0$.

$\Rightarrow {{y}^{2}}+5y-300=0$.

$\Rightarrow {{y}^{2}}+20y-15y-300=0$.

$\Rightarrow y\left( y+20 \right)-15\left( y+20 \right)=0$.

$\Rightarrow \left( y-15 \right).\left( y+20 \right)=0$.

We have y – 15 = 0 or y + 20 = 0.

We get y = 15 or y = -20.

We neglect -20 as the no. of books cannot be negative.

We substitute the value of y in equation (1).

$\Rightarrow X=\dfrac{300}{15}$.

We get X = 20.

**∴ The original list price of the book is Rs. 20.**

**Note:**We should not take negative values for total no. of books that can be bought and original list price. Whenever we get this type of problem, we need to assign the cost of one book or total books that can be bought as required for the information given in the problem. Similarly, we can expect problems to find the total no. of books that can be bought after reducing the price of books.

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