A shopkeeper buys an article for Rs 500 and sells at 20% profit — find SP and profit

Question

A shopkeeper buys an article for Rs 500 and sells it at a 20% profit. Find the Selling Price (SP) and the actual profit amount.

Solution — Step by Step

Cost Price (CP) = Rs 500
Profit percentage = 20%

We need to find: Selling Price (SP) and Profit amount.

Profit is always calculated on the Cost Price.

\text{Profit} = \frac{\text{Profit\%}}{100} \times \text{CP} = \frac{20}{100} \times 500 = \text{Rs } 100

\text{SP} = \text{CP} + \text{Profit} = 500 + 100 = \text{Rs } 600

Alternatively, use the direct formula:

\text{SP} = \frac{100 + \text{Profit\%}}{100} \times \text{CP} = \frac{120}{100} \times 500 = 1.2 \times 500 = \text{Rs } 600

Selling Price (SP) = Rs 600
Profit = Rs 100

Why This Works

Profit percentage is always calculated on CP, not SP — this is the fundamental convention in profit-and-loss. When we say “20% profit,” we mean the shopkeeper earns 20% of what he originally paid.

The multiplier method (Step 3 alternative) is faster for calculations. A 20% profit means SP is 120% of CP, so we multiply CP by $\frac{120}{100} = 1.2$ .

Alternative Method

For quick mental math, break down the percentage. 20% of 500 = 10% of 500 × 2 = 50 × 2 = 100. This avoids fractions entirely and is much faster in MCQ settings.

Common Mistake

Some students mistakenly calculate profit percentage on the Selling Price instead of the Cost Price. That would give: $\frac{20}{100} \times 600 = 120$ , making SP = 620. This is wrong. Profit% is always on CP unless the problem explicitly states otherwise.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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