Question

If an item is sold for Rs.540 at a loss of 10%, then the cost price of the item is

• A. Rs.630.
• B. Rs.610.
• C. Rs.600.
• D. Rs.620.

Hint:

A 10% loss means the item is sold at 90% of its cost price.
If 90% of $CP$ is equal to 540, then 10% of $CP$ is $540 \div 9 = 60$.
Thus, 100% of $CP$ must be $60 \times 10 = 600$. This mental math method is incredibly fast!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given the Selling Price ($SP$) of an item as Rs.540 and the loss percentage as 10%.
We need to calculate the original Cost Price ($CP$) of the item.

Step 2: Key Formula or Approach:
Profit and Loss formulas relate Cost Price, Selling Price, and Loss percentage as follows:
\[ SP = CP \times \left( \frac{100 - \text{Loss}\%}{100} \right) \]
Rearranging the formula to solve for Cost Price ($CP$):
\[ CP = \frac{SP \times 100}{100 - \text{Loss}\%} \]

Step 3: Detailed Calculation:
Substitute the given values into the formula:
- $SP = 540$
- $\text{Loss}\% = 10$
\[ CP = \frac{540 \times 100}{100 - 10} \]
\[ CP = \frac{540 \times 100}{90} \]
Simplify the fraction:
\[ CP = \frac{540}{90} \times 100 \]
Since $540 \div 90 = 6$:
\[ CP = 6 \times 100 \]
\[ CP = 600 \]

Step 4: Final Answer:
The cost price of the item is Rs.600, which corresponds to Option (C).