Step 1: Assume initial cost price

Let the initial cost price (CP) of the article be $100x$. Since the profit is $25\%$, the initial selling price ($SP_1$) is:

$SP_1 = 100x + 25\% \text{ of } 100x = 125x$

Step 2: Calculate new cost price and selling price

If he had bought it at $20\%$ less, the new cost price ($CP_2$) is $80\%$ of $100x$. If he gains $30\%$ on this new cost price, the new selling price ($SP_2$) is:

$CP_2 = 80x, \quad SP_2 = 80x \times 1.30 = 104x$

Step 3: Set up equation with selling price difference

According to the problem, the article is sold for ₹10.50 less, meaning the difference between $SP_1$ and $SP_2$ is ₹10.50:

$125x - 104x = 10.50 \implies 21x = 10.50$

Step 4: Solve for x and find Cost Price

Solving for $x$:

$x = \frac{10.50}{21} = 0.5$

Step 5: Calculate final cost price

The original cost price was $100x$:

$\text{CP} = 100 \times 0.5 = \text{₹}50$