Question

Mr. Mehra sends his servant to the market to buy oranges worth Rs. $15$. The servant has eaten 3 oranges on the way, Mr. Mehra pays $25$ paise per orange more than the market price. Find the no. of oranges which Mr. Mehra receives.

• A. $9$
• B. $11$
• C. $10$
• D. $12$

Answer 1

The correct option is D $12$

Let the number of oranges received by Mr. Mehra be x.

The cost of oranges = Rs. $\frac{15}{x}$

The number of oranges bought by servant = x + 3

The market price of orange = $\frac{15}{x+3}$

The cost paid by Mr. Mehra is 25 paise i.e., $\frac{25}{100}$ more than the market price.

So, $\frac{15}{x+3}+\frac{25}{100}=\frac{15}{x}$

$\frac{-45}{x(x+3)}=\frac{-1}{4}$

$x(x+3)=180$

$x^2+3x-180=0$
Comparing it with general form of quadratic equations $a{x}^2+bx+c=0$

Roots$=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\Rightarrow \frac{-3\pm \sqrt{(3{)}^2-4\times 1\times (-180)}}{2\times 1}$

$\Rightarrow \frac{-3\pm \sqrt{729}}{2}$

$\Rightarrow \frac{-3\pm 27}{2}$

$x=12$ or$x=-15$

Since $x$ cannot be negative, $x=12$

Number of oranges = 12.