A dealer buys two articles X and Y for ₹500 each. He marks each of them at the same price. He sells X by giving two successive discounts of 50% and 28% and still earns ₹958 as profit. If he sells Y at a single discount of 77%, then what is the profit percentage on Y?

The correct answer is 86.3%.

Step 1: Calculate the Selling Price of Article X
The cost price of article X is ₹500 and the profit earned by selling article X is ₹958.

$\text{Selling Price of X (}{\mathrm{SP}}_X\text{)}=\text{Cost Price}+\text{Profit}$

${\mathrm{SP}}_X=500+958=₹1458$

Step 2: Find the Marked Price (MP) of the articles
Article X was sold after applying two successive discounts of 50% and 28% on its marked price (MP).
The effective selling price multiplier after these two successive discounts is:

${\mathrm{SP}}_X=\mathrm{MP}\times \left(1-\frac{50}{100}\right)\times \left(1-\frac{28}{100}\right)$

${\mathrm{SP}}_X=\mathrm{MP}\times 0.50\times 0.72=\mathrm{MP}\times 0.36$

Equating this to the selling price of ₹1458:

$\mathrm{MP}\times 0.36=1458$

$\mathrm{MP}=\frac{1458}{0.36}=₹4050$

Thus, the marked price for both articles X and Y is ₹4050.

Step 3: Calculate the Selling Price of Article Y
Article Y is sold at a single discount of 77% on the marked price.



${\mathrm{SP}}_Y=4050\times 0.23=₹931.50$

Step 4: Calculate the Profit Percentage on Article Y
The cost price of article Y is ₹500.

$\text{Profit on Y}={\mathrm{SP}}_Y-\text{Cost Price}=931.50-500=₹431.50$

Now, calculate the profit percentage:

$\text{Profit Percentage}=\left(\frac{\text{Profit on Y}}{\text{Cost Price}}\right)\times 100$

$\text{Profit Percentage}=\left(\frac{431.50}{500}\right)\times 100=\frac{431.50}{5}=86.3\%$

Therefore, the profit percentage earned on article Y is 86.3%.