A potter makes more than $100$ but less than $300$ pots and arranges them in rows, with each row consisting of the same number of pots, for drying. He finds that if he places $6$ pots more per row, he can arrange the pots in $10$ less rows. How many pots does the potter make?
The answer to this question is given as $225$ but I obtained $120$ also as one of the possible solutions.
Is $120$ wrong? If yes, why?
Here's how I obtained the solutions:
Let the number of rows be $n$ and the number of pots per row be $x$ the we have $$nx=(n-10)(x+6)$$ Which is same as $$3n-5x=30$$ Solving it as a Diophantine equation, we obtain solutions for $(n,x)$ as $(10,0), (15,3), (20,6), (25,9), (30,12), \dots$
Since $100<nx<300$ so, we have solutions as $(20,6)$ and $(25,9)$.