Question

A man could buy a certain number of notebooks for $Rs.300$. If each notebook cost is $Rs.5$ more, he could have bought $10$ notebooks less for the same amount. Find the price of each notebook?

• A. $10$
• B. $15$
• C. $8$
• D. $7.50$

Answer 1

Answer: (A)

$10$

Let the price of each notebook be Rs.x.
Let the number of notebooks which can be brought for Rs.$300$ each at a price of Rs.x be y.
Hence $xy$ = $300$
$y=\frac{300}{x}$

According to the question:
$\Rightarrow (x+5)(y-10)=300$
$\Rightarrow xy+5y-10x-50=xy$
$\Rightarrow 5\frac{300}{x}-10x-50=0$
$\Rightarrow -150+x^2+5x=0$

$\Rightarrow x^2+15x-10x-150=0$
$\Rightarrow x(x+15)-10(x+15)=0$
$\Rightarrow x=10$ or $-15$
Price cannot be negative
So, As $x>0,x=10$.