First Principles AI

Solution

Let the number of sheep bought be $x$ .

Price per sheep:

\frac{9000}{x}

If he paid Rs. 100 less per sheep, new price per sheep is:

\frac{9000}{x}-100

Then he would get $x+3$ sheep for Rs. 9000:

(x+3)\left(\frac{9000}{x}-100\right)=9000

Expand:

9000+\frac{27000}{x}-100x-300=9000

\frac{27000}{x}-100x-300=0

Multiply by $x$ :

27000-100x^2-300x=0

Divide by $-100$ :

x^2+3x-270=0

(x+18)(x-15)=0

So $x=-18$ or $x=15$ . Reject $x=-18$ .

\boxed{x=15}

\boxed{\text{The farmer bought 15 sheep.}}