First Principles AI

Solution

Let the number of dozen eggs sold be $x$ .

Price per dozen:

\frac{2400}{x}

If he had 2 dozen more, total would be $x+2$ dozen.

He would get the same money by selling at Rs. 0.50 cheaper per dozen:

\frac{2400}{x}-\frac{2400}{x+2}=\frac{1}{2}

Multiply by $2x(x+2)$ :

4800(x+2)-4800x=x(x+2)

9600=x^2+2x

x^2+2x-9600=0

(x-96)(x+100)=0

Reject $x=-100$ .

\boxed{x=96}

\boxed{\text{He sold 96 dozen eggs.}}