Question

A shopkeeper marks an article at Rs 2,500 and offers a discount of 20%. If the cost price of the article is Rs 1,700, what is the profit percentage earned?

• A. 15.5%
• B. 17.6%
• C. 20%
• D. 22.4%

Hint:

Always remember that discount is computed on the Marked Price ($MP$), while profit or loss percentage is calculated on the Cost Price ($CP$).
To speed up calculations during the exam, use multiplier decimals: a 20% discount is equivalent to multiplying the $MP$ by 0.8 directly, which yields the $SP$ instantly.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question is based on the concept of Profit, Loss, and Discount in commercial arithmetic.
The shopkeeper lists an article at a specific price, known as the Marked Price.
A discount is a reduction offered on this Marked Price, which determines the actual Selling Price.
The Cost Price represents the initial investment made by the shopkeeper to acquire the article.
Our goal is to find the net profit percentage, which is the percentage of profit earned relative to the Cost Price.

Step 2: Key Formula or Approach:
We will use the following standard mathematical formulas:
1. Selling Price ($SP$) after discount:
\[ SP = MP \times \left(1 - \frac{\text{Discount \%}}{100}\right) \]
2. Absolute Profit made on the transaction:
\[ \text{Profit} = SP - CP \]
3. Profit Percentage calculated on the Cost Price:
\[ \text{Profit \%} = \left(\frac{\text{Profit}}{CP}\right) \times 100\% \]

Step 3: Detailed Explanation:
$\bullet$ Let us write down the given parameters from the question statement.
$\bullet$ The Marked Price ($MP$) of the article is given as Rs 2,500.
$\bullet$ The Discount percentage ($D\%$) offered by the shopkeeper is 20%.
$\bullet$ The Cost Price ($CP$) of the article is given as Rs 1,700.
$\bullet$ First, we compute the Selling Price ($SP$) using the marked price and discount percentage:
\[ SP = 2500 \times \left(1 - \frac{20}{100}\right) \]
\[ SP = 2500 \times 0.80 \]
\[ SP = 2000 \]
$\bullet$ So, the actual Selling Price of the article after the discount is Rs 2,000.
$\bullet$ Next, we determine the absolute profit earned by subtracting the Cost Price from this Selling Price:
\[ \text{Profit} = SP - CP \]
\[ \text{Profit} = 2000 - 1700 = 300 \]
$\bullet$ To find the profit percentage, we express this profit as a percentage of the Cost Price:
\[ \text{Profit \%} = \left(\frac{300}{1700}\right) \times 100\% \]
\[ \text{Profit \%} = \frac{300}{17}\% \approx 17.647\% \]
$\bullet$ On rounding this value to one decimal place, we obtain approximately 17.6%.

Step 4: Final Answer:
The final profit percentage earned by the shopkeeper is approximately 17.6%.
Hence, the correct option is (B).