Maths Olympiad · topic 15 of 33 · free

Percentages, profit and loss — Maths Olympiad practice

Percentage questions are about “out of 100”. In profit and loss, the commonest trap is dividing by the selling price; profit and loss percent are always taken on the cost price. A discount is taken off the marked price.

How to solve it

Always out of the cost — “profit % and loss % are worked out on the cost price, never the selling price”

  1. p% of N = N × p ÷ 100.
  2. Profit = selling price − cost price; profit % = profit ÷ cost price × 100 (loss works the same way).
  3. Discount = p% of the marked price; selling price = marked price − discount.

Use it for: Shopping, marks, discounts and profit-and-loss questions in Class 7–10.

Worked example: A shopkeeper buys a toy for ₹400 and sells it for ₹460. What is his profit percent? 15%

  1. Profit = ₹460 − ₹400 = ₹60.
  2. Profit % = 60 ÷ 400 × 100 = 15%.

Check: 15% of ₹400 = ₹60, and ₹400 + ₹60 = ₹460 ✓

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