The percentage profit earned when an article is sold for Rs. 780 is double the percentage profit earned when the same article is sold for Rs. 470. If the marked price of the article is 25% above the cost price, then what is the marked price of the article?

To find the marked price of the article, we can break down the problem into step-by-step calculations: finding the cost price first, and then using it to calculate the marked price.

Step 1: Set up the relation for Cost Price (CP)
Let the cost price of the article be $C$ rupees.
The formula for percentage profit is given by:

$\text{Percentage Profit}=\frac{\text{Selling Price (SP)}-\text{Cost Price (C)}}{\text{Cost Price (C)}}\times 100$

According to the problem, the percentage profit when sold for Rs. 780 is double the percentage profit when sold for Rs. 470.
Therefore, we can write the equation as:

$\frac{780-C}{C}\times 100=2\times \left(\frac{470-C}{C}\times 100\right)$

Step 2: Solve for Cost Price (CP)
We can simplify the equation by dividing both sides by $\frac{100}{C}$:

$780-C=2\times (470-C)$

Expanding the right side:

$780-C=940-2C$

Rearranging the terms to solve for $C$:

$2C-C=940-780$

$C=160$

So, the cost price of the article is Rs. 160.

Step 3: Calculate the Marked Price (MP)
The marked price is 25% above the cost price.

$\text{Marked Price}=C+25\%\text{of}C$

Substituting $C=160$ into the equation:

$\text{Marked Price}=160+\left(\frac{25}{100}\times 160\right)$

$\text{Marked Price}=160+40=200$

Thus, the marked price of the article is Rs. 200.