Quantitative aptitude · lesson 12 of 30 · free

Profit and loss — Quantitative aptitude for kids

A shopkeeper buys at the cost price (CP) and sells at the selling price (SP). If SP is more, there is a profit; if less, a loss. Profit and loss percent are always worked out on the cost price.

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The method

Cost price is 100% — “profit % and loss % are always worked out on the cost price”

  1. Profit = SP − CP; loss = CP − SP.
  2. Profit % = profit ÷ CP × 100 (same for loss %).
  3. SP = CP × (100 + profit%) ÷ 100, or CP × (100 − loss%) ÷ 100.
  4. CP from SP: CP = SP × 100 ÷ (100 + profit%) or SP × 100 ÷ (100 − loss%).

Use it for: Shopping, running a stall at a school fair, business maths in Class 7–10, and aptitude tests.

🧮 Check your own sums with the free Profit and loss calculator — it shows the working.

Worked example: By selling a watch for ₹1150, a shopkeeper makes a profit of 15%. What did the watch cost the shopkeeper (in ₹)? → 1000

  1. Take CP as 100%; SP is 115% of it.
  2. CP = 1150 × 100 ÷ 115 = ₹1000.

Check: 15% of ₹1000 = ₹150, and 1000 + 150 = 1150 ✓

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