Answer: Option B
Given information:

• Selling price of the article = Rs 312.50
• Actual profit = 20%

The student has calculated the profit percentage on the selling price instead of the cost price. Let's say the cost price of the article is Rs x. Then, the selling price is Rs (x + 0.2x) = Rs 1.2x.
We are given that the selling price is Rs 312.50. So, we can write:
1.2x = 312.50x = 312.50/1.2x = 260.4167
Therefore, the cost price of the article is Rs 260.4167.
Now, let's calculate the profit percentage on the selling price as calculated by the student. The profit as calculated by the student is the difference between the selling price and the cost price.
Profit = Selling price - Cost priceProfit = Rs 312.50 - Rs 260.4167Profit = Rs 52.0833
The profit percentage on the selling price as calculated by the student is given by the formula:
Profit percentage = (Profit/Selling price) x 100
Substituting the values, we get:
Profit percentage = (52.0833/312.50) x 100Profit percentage = 16.6667%
Therefore, the profit calculated by the student is 16 2/3 % (Option B).
To summarize:

• Cost price of the article = Rs 260.4167
• Selling price of the article = Rs 312.50
• Actual profit = 20%
• Profit calculated by the student = 16 2/3 %

Important Definitions:

• Cost Price: The amount paid to purchase an item or the cost incurred to produce an item.
• Selling Price: The amount at which an item is sold.
• Profit: The difference between the selling price and the cost price.
• Profit Percentage: The percentage of profit earned on the cost price or the selling price, expressed as a percentage of the cost price or the selling price.

If you think the solution is wrong then please provide your own solution below in the comments section .