A group of friends split a ₹1,200 restaurant bill equally. Had 2 more friends joined them, each person would have paid ₹50 less. How many friends were in the group?

Explanation

1. 01

   With $n$ friends each pays $\frac{1200}{n}$; with $n + 2$ each pays $\frac{1200}{n + 2}$.

2. 02

   $\frac{1200}{n} - \frac{1200}{n + 2} = 50$, so $\frac{2400}{n(n + 2)} = 50$ and $n(n + 2) = 48$.

3. 03

   $n^2 + 2n - 48 = 0$ gives $(n + 8)(n - 6) = 0$, so $n = 6$.

4. 04

   Check: ₹200 each for 6 people, ₹150 each for 8.