CMAT 2013 Solved Question Paper

(b) Let the Shopkeeper buys x books.
∴ Rate of the book = 80 / x
The new number of books = (x + 4)
∵ The new price = 80 / (x + 4)
∴ $\frac{80}{\left(\mathit{x}+4\right)}$ + 1 = $\frac{80}{\mathit{x}}$
⇒ $\left(\frac{1}{\mathit{x}}-\frac{1}{\left(\mathit{x}+4\right)}\right)$ = $\frac{1}{80}$
⇒ $\frac{4}{{\mathit{x}}^2+4\mathit{x}}$ = $\frac{1}{80}$
⇒ ${\mathit{x}}^2$ + 4x - 320 = 0
⇒ (x + 20) (x - 16) = 0
∴ x = 16 (∵ x = - 20 is inadmissible)
So, he bought 16 books.