An article costing ₹80 was marked 25% above the cost price. After offering a discount of X%, the customer now pays ₹81. If the marked price is increased twice successively by X% and the article is sold at the new marked price, then the profit would be what percent more than the profit when the selling price was ₹81?

The Cost Price (CP) of the article is $₹80$.

The article was marked 25% above the CP.

$\text{MP} = \text{CP} + 25\% \text{ of CP}$

$\text{MP} = 80 + \frac{25}{100} \times 80$

$\text{MP} = 80 + \frac{1}{4} \times 80$

$\text{MP} = 80 + 20$

$\text{MP} = ₹100$

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The article was sold for a Selling Price (SP) of $₹81$ after a discount of $X\%$ on the MP.

$\text{Discount} = \text{MP} - \text{SP}$

$\text{Discount} = 100 - 81$

$\text{Discount} = ₹19$

The discount percentage $X\%$ is calculated on the MP:

$X\% = \frac{\text{Discount}}{\text{MP}} \times 100$

$X = \frac{19}{100} \times 100$

$X = 19$

So, the discount percentage is $19\%$.

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The original marked price $(\text{MP}_1)$ is $₹100$.

The marked price is increased twice successively by $X\% = 19\%$.

$\text{New Marked Price } (\text{MP}_2) = \text{MP}_1 \left(1 + \frac{X}{100}\right) \left(1 + \frac{X}{100}\right)$

$\text{MP}_2 = 100 \left(1 + \frac{19}{100}\right) \left(1 + \frac{19}{100}\right)$

$\text{MP}_2 = 100 \left(\frac{119}{100}\right) \left(\frac{119}{100}\right)$

$\text{MP}_2 = \frac{119 \times 119}{100}$

$\text{MP}_2 = \frac{14161}{100}$

$\text{MP}_2 = ₹141.61$

The article is now sold at this new marked price, so the New Selling Price $(\text{SP}_2)$ is $₹141.61$.

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The Cost Price (CP) remains $₹80$.

When SP was $₹81$:

$\text{Profit}_1 = \text{SP}_1 - \text{CP}$

$\text{Profit}_1 = 81 - 80$

$\text{Profit}_1 = ₹1$

When SP is $₹141.61$:

$\text{Profit}_2 = \text{SP}_2 - \text{CP}$

$\text{Profit}_2 = 141.61 - 80$

$\text{Profit}_2 = ₹61.61$

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The percentage by which $\text{Profit}_2$ is more than $\text{Profit}_1$:

$\text{Increase in Profit} = \text{Profit}_2 - \text{Profit}_1$

$\text{Increase in Profit} = 61.61 - 1$

$\text{Increase in Profit} = ₹60.61$

$\text{Required Percentage} = \frac{\text{Increase in Profit}}{\text{Profit}_1} \times 100$

$\text{Required Percentage} = \frac{60.61}{1} \times 100$

$\text{Required Percentage} = 6061\%$

Therefore, the profit would be $6061\%$ more than the profit when the selling price was $₹81$.