Question

A businessman knows that the price of a commodity will increase by $\text{Rs}5$ per packet. He bought some packets of this commodity for $\text{Rs}4500$. If he bought this packet at the new price, then he gets $10$ packets less. What is the number of packets bought by him?

• A. $100$
• B. $72$
• C. $84$
• D. $97$

Answer 1

The correct option is A $100$

Let the number of packets purchased by the businessman be x.

Total price of $x$ packets is $\text{Rs}4500$

$⟹$ price of each packet $=\frac{4500}{x}$

If the price of each packet increases by $\text{Rs}5$ then new price of each packet $=\frac{4500}{x}+5$

Now, number of packets that can be bought in $\text{Rs}4500$ at new price $=\frac{4500}{\frac{4500}{x}+5}$

As per the question,

$\frac{4500}{\frac{4500}{x}+5}=x-10$

$\Rightarrow \frac{4500x}{4500+5x}=x-10$

$\Rightarrow 4500x=4500x+5x^2-45000-50x$

$\Rightarrow x^2-10x-9000=0$

Using $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ to find the roots of the quadratic equation

$\Rightarrow x=\frac{10\pm \sqrt{(-10{)}^2-4\times 1\times (-9000)}}{2\times 1}$

$\Rightarrow x=\frac{10\pm \sqrt{36100}}{2}$

$\Rightarrow x=\frac{10\pm 190}{2}$

$x=100$, $x=-90$

$x$ cannot be negative.

Number of packets $=100$.