Explanation:

- Let's denote the cost price of the article as Rs "C".

- The selling price at 5.75% profit is C + 5.75% of C = C × 1.0575.

- If sold at 1.2% loss, selling price is C - 1.2% of C = C × 0.988.

- The difference between these two selling prices is Rs 1,390, hence:

$C\times 1.0575-C\times 0.988=Rs1,390$.

- This simplifies to $C\times 0.0695=Rs1,390$.

- Solve for C: $C=Rs1,390/0.0695=Rs20,000$.

- So, Option 3: Rs 20,000 is the correct cost price.