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Three percentage calculations in one place — X% of Y, shares, and percentage change.
Shopping discount: a jacket costs ₹1,499 with “20% off”. 20% of 1499 = 299.8, so you pay ₹1,199.20.
Exam marks: you scored 415 out of 500. 415 ÷ 500 × 100 = 83%.
Price rise: petrol goes from ₹96.70 to ₹102.30. Change = (102.30 − 96.70) ÷ 96.70 × 100 = 5.79% increase.
Salary hike: ₹45,000 to ₹52,000 = (52000 − 45000) ÷ 45000 × 100 = 15.56% increase.
Percentage increase and decrease are not symmetric. If a price rises 25% and then falls 25%, you do not return to the start — ₹100 → ₹125 → ₹93.75. Always divide by the correct base: the old value for increase/decrease, and the “of” number for shares.
10% = move the decimal one place left (10% of 460 = 46). 5% = half of 10%. 15% = 10% + 5%. 20% = 10% doubled. Most restaurant tips and discounts can be done in your head this way.
If an interest rate rises from 8% to 10%, that is a rise of 2 percentage points, but a 25% increase in the rate. News headlines and loan advertisements routinely blur this distinction. A 2 percentage point hike on a 10 lakh loan at 9% versus 11% changes your 20-year EMI by roughly 1,400 a month — understanding the difference saves real money.
Another classic confusion: a 50% loss needs a 100% gain to recover. If your 1,00,000 rupee portfolio falls 50% to 50,000, it must double — a full 100% gain — to get back to 1,00,000.
Board marks are the classic use: 465 out of 500 is simply (465/500) x 100 = 93%. Under the older CBSE CGPA system, the accepted conversion was percentage = CGPA x 9.5, so a CGPA of 8.4 meant about 79.8%.
Successive percentage changes multiply, they do not add. A 20% discount followed by an extra 10% off is not 30% off: you pay 0.8 x 0.9 = 0.72, i.e. 28% off. The same logic governs successive hikes — 10% inflation two years in a row raises prices 21%, not 20%.
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