Question

If the price of book is reduced by 75. A person can 4 more books for 600. Find the original price of a book. Anyone can answer there are brilliant​

Answer 1

Given Question :

If the price of book is reduced by 75. A person can buy 4 more books for 600.

To Find :

The original price of the book

Solution :

Let the original price of the book be x.

Then,

Original Price = x

And, when price of book is reduced by 75 then the price becomes (x-75).

Total cost of books = 600

Now, According to the question

$\frac{600}{x - 75} - \frac{600}{x } = 4$

$\frac{600x - 600(x - 75)}{x(x - 75 )} = 4 \\ \\ \frac{600x - 600x + 45000}{ {x}^{2} - 75x} = 4 \\ \\ 45000 = 4( {x}^{2} - 75x) \\ \\ 45000 = 4 {x}^{2} - 300x \\ \\ 0 = 4 {x}^{2} - 300x - 45000$

On solving this by middle term factorization,

4x²-300x - 45000 =0

x ² - 75 x- 11250 = 0

x ² + 75x - 150x - 11250 = 0

x (x+75) - 150(x+75) = 0

(x - 150)(x+75) = 0

As price can't be a negative value then,x =150 .

Therefore, the original price of the book is 150 rupees.