Solve: if cost price is ₹500 and selling price is ₹575, find profit percentage

Question

A shopkeeper buys an article for ₹500 (cost price) and sells it for ₹575 (selling price). Find the profit and profit percentage.

(NCERT Class 7)

Solution — Step by Step

Since SP > CP, there is a profit:

$\text{Profit} = \text{SP} - \text{CP} = 575 - 500 = \mathbf{\text{₹}75}$

Profit percentage is always calculated on the cost price:

\text{Profit \%} = \frac{\text{Profit}}{\text{CP}} \times 100 = \frac{75}{500} \times 100 = \mathbf{15\%}

Why This Works

Profit percentage tells us how much profit was made for every ₹100 invested. A 15% profit means the shopkeeper earned ₹15 for every ₹100 of cost. We use CP as the base (denominator) because profit is calculated relative to what was spent, not what was received.

Verification: 15% of ₹500 = $\frac{15}{100} \times 500 = \text{₹}75$ . Adding to CP: $500 + 75 = \text{₹}575$ = SP. Correct!

Alternative Method — Direct Formula

\text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right)

575 = 500 \times \left(1 + \frac{P}{100}\right)

\frac{575}{500} = 1 + \frac{P}{100} \implies 1.15 = 1 + \frac{P}{100} \implies P = 15\%

For quick mental math: ₹75 profit on ₹500 = ₹75/₹5 per ₹100 = ₹15 per ₹100 = 15%. Dividing both numerator and denominator by 5 simplifies the calculation.

Common Mistake

Students sometimes calculate profit percentage on the selling price instead of the cost price. The formula is $\frac{\text{Profit}}{\text{CP}} \times 100$ , NOT $\frac{\text{Profit}}{\text{SP}} \times 100$ . Using SP in the denominator gives $75/575 \times 100 = 13.04\%$ , which is wrong. Profit and loss percentages are always on CP unless stated otherwise.

Question

Solution — Step by Step

Why This Works

Alternative Method — Direct Formula

Common Mistake

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