Question

An item costs Rs. 250. If the item is sold for Rs.280, then the profit percentage is

• A. 12%
• B. 15%
• C. 20%
• D. 10%

Hint:

Always calculate profit percentage using the Cost Price as your base: \[ \text{Profit \%} = \frac{\text{Gain}}{\text{C.P.}} \times 100 = \frac{30}{250} \times 100 = 12\% \]

Answer 1

The Correct Option is A

Concept: In commercial arithmetic, when the Selling Price (S.P.) of a commodity exceeds its initial Cost Price (C.P.), the transaction results in a financial profit. The standard formulas are defined as follows: \[ \text{Profit} = \text{Selling Price (S.P.)} - \text{Cost Price (C.P.)} \] \[ \text{Profit Percentage } (\%) = \left( \frac{\text{Profit}}{\text{Cost Price (C.P.)}} \right) \times 100 \]

Step 1: Extract parameters and calculate the absolute profit amount.
From the problem statement, we have:
• Cost Price (C.P.) = Rs. 250
• Selling Price (S.P.) = Rs. 280 Substitute these parameters into the absolute profit formula: \[ \text{Profit} = 280 - 250 = \text{Rs. } 30 \]

Step 2: Calculate the profit percentage based on the Cost Price.
Substitute the profit value and the original Cost Price into our percentage formula: \[ \text{Profit Percentage} = \left( \frac{30}{250} \right) \times 100 \] Let us simplify this step-by-step by canceling out common factors: \[ \text{Profit Percentage} = \frac{30 \times 100}{250} \] Divide the numerator and denominator by 50: \[ 100 \div 50 = 2 \] \[ 250 \div 50 = 5 \] This simplifies the equation to: \[ \text{Profit Percentage} = \frac{30 \times 2}{5} = \frac{60}{5} \] Performing the final division: \[ 60 \div 5 = 12\% \] Hence, the profit percentage realized from this transaction is exactly 12%, aligning with Option (A).