Question

An article is sold for Rs. 2000 with profit of 25%. What would have been the percentage of profit, if it was sold for Rs. 1800?

• A. 10%
• B. 11%
• C. 12.5%
• D. 13.5%

Hint:

First find the cost price using \(CP = \frac{2000 \times 100}{125}\), then work out the profit percent on Rs. 1800.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The article was sold at Rs. 2000 and this gave a profit of 25 percent. From this we can find the cost price. Then we find the profit percentage when the selling price is Rs. 1800.

Step 2: Key Formula or Approach:
Profit percent is always taken on the cost price.
\[ \text{Profit percent} = \frac{SP - CP}{CP} \times 100 \]
\[ CP = \frac{SP \times 100}{100 + \text{Profit percent}} \]

Step 3: Find the cost price:
With a profit of 25 percent, the selling price is 125 percent of the cost price.
\[ CP = \frac{2000 \times 100}{125} = 1600 \]
So the cost price is Rs. 1600.

Step 4: Find the new profit:
Now the selling price is Rs. 1800.
Profit = \(1800 - 1600 = 200\).
\[ \text{Profit percent} = \frac{200}{1600} \times 100 = 12.5 \]
So the profit is 12.5 percent.

Step 5: Check the wrong options:
10 percent would need a selling price of Rs. 1760. 11 percent would need Rs. 1776. 13.5 percent would need Rs. 1816. None of these equals Rs. 1800, so options (1), (2) and (4) are wrong.

Final Answer:
The profit would have been 12.5 percent. This is option (3). \[ \boxed{12.5 \%} \]