Question

A shopkeeper earns 20% profit on an article whose cost price is Rs 800. Find the selling price.

• A. Rs 920
• B. Rs 940
• C. Rs 960
• D. Rs 1000

Hint:

For a \( 20% \) increase, you can directly multiply the original amount by \( 1.2 \).
Calculation: \( 800 \times 1.2 = 960 \) can be done mentally in seconds.
This multiplier method is extremely useful for profit, loss, and percentage increase problems.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This is a commercial arithmetic problem dealing with cost price, selling price, and profit percentage.
The shopkeeper bought an item for a certain amount (Cost Price) and sold it to make a specified profit percentage.
We need to determine the final Selling Price.

Step 2: Key Formula or Approach:
We can solve this problem using either of the following two standard formulas:
Method 1: Calculate the absolute profit value and add it to the cost price:
\[ \text{Profit} = \frac{\text{Profit Percentage}}{100} \cdot CP \]
\[ SP = CP + \text{Profit} \]
Method 2: Use the direct multiplier formula for selling price:
\[ SP = CP \cdot \left( 1 + \frac{\text{Profit Percentage}}{100} \right) \]
where:
- \( CP \) is the Cost Price.
- \( SP \) is the Selling Price.

Step 3: Detailed Explanation:
Let us list the given parameters:
- Cost Price, \( CP = 800 \)
- Profit Percentage = \( 20% \)
Let us calculate using Method 1:
First, find the absolute profit earned by the shopkeeper:
\[ \text{Profit} = \frac{20}{100} \cdot 800 \] Simplifying this calculation:
\[ \text{Profit} = 0.20 \cdot 800 = 160 \]
So, the shopkeeper earned a profit of Rs 160.
Now, calculate the Selling Price by adding the profit to the Cost Price:
\[ SP = CP + \text{Profit} \] \[ SP = 800 + 160 = 960 \]
Let us calculate using Method 2 to verify:
\[ SP = 800 \cdot \left( 1 + \frac{20}{100} \right) \] \[ SP = 800 \cdot (1 + 0.20) \] \[ SP = 800 \cdot 1.20 = 960 \]
Both methods yield the same selling price of Rs 960.
Let us review why the other options are incorrect:
- Option (A) Rs 920 is incorrect because it corresponds to a profit percentage of only \( 15% \).
- Option (B) Rs 940 is incorrect because it corresponds to a profit percentage of \( 17.5% \).
- Option (D) Rs 1000 is incorrect because it corresponds to a profit percentage of \( 25% \).

Step 4: Final Answer:
The selling price of the article is Rs 960, which corresponds to Option (C).