Question

A student purchase some books for $Rs1600$. If he had bought $8$ more books for the same amount each book would cost $Rs10$ less. The number of books he buys is

• A. $30$
• B. $32$
• C. $34$
• D. $36$

Answer 1

The correct option is A $30$

Given that,

A student purchase books for $Rs.1600$

Let the number of books purchased for $Rs.1600=x$

Then,

The cost of each books $=\frac{1600}{x}$

If he buys for more books, the number of books$=x+8$

Cost of each book $=\frac{1600}{x+4}$

$\begin{array}{c}\Rightarrow \left(\frac{1600}{x}\right)-\left[\frac{1600}{x+4}\right]=1\\ \Rightarrow \frac{1600\left(x+4\right)-1600x}{x\left(x+4\right)}=1\end{array}$

$\Rightarrow \frac{1600x+6400-1600x}{x^2+4x}=1$

$\Rightarrow \frac{6400}{x^2+4x}=1$

$x^2+4x-6400=0$

$x=-2-2\sqrt{1601}$

$x=-2+2\sqrt{1601}$

Then,

we get the number of books purchased $x=-2+2\sqrt{1601}$

Option $A$ is correct answer.