Question

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

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\small{\underline{\green{\rm{Given:}}}}$

• $\rm{The\: price\:of\:a\: book\:is\: reduced\:by\:75}$
• $\sf{A\:man\:can\:buy\:4\:more\: books\:for\:Rs.600}$

$\large{\underline{\red{\rm{let:}}}}$

• $\sf{The\: orginal\: price\:of\:book=x}$
• $\sf{The\: price\: books\: after\: buying\:at\: orginal\: price=\dfrac{600}{x}}$
• $\sf{The\: price\: books\: after\: reducing=x-75}$

$\small{\underline{\orange{\rm{To\: Find:}}}}$

• $\sf{The\: orginal\: price\:of\:the\:book=?}$

$\small{\underline{\red{\rm{According\:to\: above\: information:}}}}$

$\rm{\implies \dfrac{600}{x-75}-\dfrac{600}{x}=4}$

$\rm{\implies \dfrac{600x-600x+45000}{(x)(x-75)}=4}$

$\rm{\implies 4x^2-300x=45000}$

$\rm{\implies 4x^2-300x-45000=0}$

• $\sf{Dividing\:by\:4\:on\:both\:side}$

$\rm{\implies x^2-75x-11250=0}$

$\rm{\implies x^2+75x-150x-11250=0}$

$\rm{\implies x(x+75)-150(x+75)=0}$

$\rm{\implies (x-150)(x+75)=0}$

• $\rm{\therefore x-150=0=>x=150}$
• $\rm{\therefore x+75=0=>x=-75}$

Here, negative value can't be the original price of book so we take x=150

Hence,

$\sf\green{The\: orginal\: price\:of\:the\:book=Rs.150}$

Answer 2

$= > \frac{600}{x - 75} - \frac{600}{x} = 4 \\ = > \frac{600x - 600x + 45000}{x(x - 75)}=4 \\ 4{x}^{2} - 300x - 45000 = 0 \\ {x}^{2} - 75x - 11250 = 0 \\ {x}^{2} + 75x - 150x - 11250 = 0 \\ x(x + 75)- 150(x + 75) = 0 \\ x - 150 = 0 \\ x = 150 \\ x + 75 = 0 \\ x = - 75$

therefore, orginal price of book =150