Question

If the price of a book is reduced by Rs. 5, a person can buy 5 more books for Rs. 300. Find the original list price of the book.

Answer 1

Hint: At first, take the original list price as x, so the number of books one can buy is \[\dfrac{300}{x}\]. Now after decreasing the price by 5, the number of books can be bought is \[\dfrac{300}{x-5}\]. Now, read the question and proceed accordingly.

Complete step-by-step answer:
In the question, we are given a relation of the cost of the books and the number of books. The condition is given that if the shopkeeper lowers the price of the books by 5, then the person can buy 5 more books for Rs. 300. So, at first, let’s assume that the list price of the books is Rs. x.
Now for finding the number of boos, we will apply the formula that the number of books is equal to \[\dfrac{\text{Total Amount}}{\text{Amount of a single book}}\]
The amount of books is x, then the person can find the number of books by dividing 300 by x. So, we get, \[\dfrac{300}{x}\]. Now, as the price of each book is decreased by 5, we can write it as (x – 5), then the person can find the number of books by dividing 300 by (x – 5). So, we get, \[\dfrac{300}{x-5}\].
Now, from these, we can form an equation according to the condition given. So, we can form the equation as,
\[\dfrac{300}{x-5}-\dfrac{300}{x}=5\]
Now, taking the LCM, we get,
\[\dfrac{300x-300\left( x-5 \right)}{x\left( x-5 \right)}=5\]
On cross multiplying we get,
\[1500=5x\left( x-5 \right)\]
Now, on further simplifying and reversing the equation, we get,
\[5{{x}^{2}}-25x=1500\]
Now, taking 1500 to the left side, we get,
\[5{{x}^{2}}-25x-1500=0\]
Now by dividing by 5 throughout the equation, we get,
\[{{x}^{2}}-5x-300=0\]
Now using the middle term further and factorising, we get,
\[{{x}^{2}}-20x+15x-300=0\]
So now on factorising, we get,
\[\left( x+15 \right)\left( x-20 \right)=0\]
So, the values of x for which it satisfies the equation are – 15 and 20. But as we took x as the original list price, Price can’t be negative so, we reject the negative answer. Hence, x is Rs. 20.
Therefore, the original list price is Rs. 20.

Note: Students should read the question twice before solving it because the language of questions forms the equations. They should also be careful while factorizing it and taking the values of x as x can only be considered positive or both.