Questions & Answers

Question

Answers

Answer
Verified

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.