Question

If the price of a book is reduced by Rs.5, a person can buy 4 more books for Rs.600. Find the original price of the book.

Answer 1

Let the prize of one book be Rs. x

let the no. of books be y

so total amount spent = xy

600 =xy

now changed price of book = Rs. (x -5)

no. of books bought = y + 4

so total amount spent = (x - 5)(y + 4)

$600=xy+4x-5y-20620=600+4x-5y4x-5y=205y=4x-20y=\frac{4x-20}{5}$

now putting this in xy = 600

$x\left(\frac{4x-20}{5}\right)=6004x^2-20x=30004x^2-20x-3000=0x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{20\pm \sqrt{(-20{)}^2-4(4\left)\right(-3000)}}{2\times 4}=\frac{20\pm \sqrt{400+48000}}{8}=\frac{20\pm \sqrt{48400}}{8}=\frac{20\pm 220}{8}=\frac{20+220}{8}or\frac{20-220}{8}=\frac{240}{8}or\frac{-200}{8}=30or-25$

Price of book cannot be negative so x is not equal to -25

so actual cost of book is x= Rs. 30