Question

A shopkeeper sold an item for Rs. 440 at a 10% profit. What was the Cost Price?

• A. Rs. 400
• B. Rs. 396
• C. Rs. 410
• D. Rs. 380

Hint:

CP = [SP / (100 + Profit%)] $\times$ 100.

Answer 1

The Correct Option is A

Step 1: Understand the Concept
This problem is based on the core principles of Profit and Loss. When an item is sold at a profit, the Selling Price (SP) is equal to the original Cost Price (CP) plus the profit earned. Because profit is always calculated as a percentage of the Cost Price, making a 10% profit means the final Selling Price is exactly 110% of the Cost Price.

Step 2: Identify Given Information & Analyze
Based on the problem, we have the following values:
Selling Price (SP) = Rs. 440
Profit Margin = 10%
Applying our concept, we can set up the relationship: SP = 110% of CP.
Written mathematically, this becomes:
$440 = \frac{110}{100} \times CP$

Step 3: Calculation & Conclusion
To find the actual Cost Price, we simply rearrange the equation to solve for CP:
$CP = \frac{440 \times 100}{110}$
By dividing 440 by 110, we get 4. Multiplying that by 100 gives us our final value:
$CP = 4 \times 100 = 400$
Therefore, the original Cost Price of the item was Rs. 400.

Final Answer: (A)