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Apply percentage formulas such as percent of number, ratio to percent, or successive change.
FAQ
Common questions and clear answers for this topic.
Percentage means per hundred and is used to express a number as a fraction of 100. Formula: Percentage = (Value/Total Value) x 100. In competitive exams like SSC CGL, IBPS Bank PO, and CAT, percentage questions appear as: finding percentage of a number, percentage increase/decrease, percentage change, successive percentage change, and percentage in Data Interpretation.
Important percentage-fraction equivalents: 10% = 1/10, 12.5% = 1/8, 16.67% = 1/6, 20% = 1/5, 25% = 1/4, 33.33% = 1/3, 37.5% = 3/8, 50% = 1/2, 62.5% = 5/8, 66.67% = 2/3, 75% = 3/4. Converting percentages to fractions makes calculations faster. For example: 25% of 480 = 480/4 = 120. Memorizing these fractions is essential for quick Quantitative Aptitude calculations.
Percentage Increase = (Increase/Original Value) x 100. Percentage Decrease = (Decrease/Original Value) x 100. If price increases by x% then decreases by x%, net effect is a decrease of x squared/100 percent. For Successive Percentage Changes: if first change is a% and second is b%, overall change = a + b + (ab/100) percent. This formula is crucial for profit/loss and interest problems in competitive exams.
Population problems use percentage increase formula. If population is P and annual growth rate is r%, then after n years: Population = P x (1 + r/100)^n. Example: Town population 50,000 grows at 10% per year. After 2 years = 50000 x 1.1 x 1.1 = 60,500. If growth rate decreases, use (1-r/100). These problems appear in SSC CGL, IBPS, and banking exams.
Shortcut methods: 1) For 1%: divide by 100, 2) For 10%: divide by 10, 3) For 5%: divide by 20 (half of 10%), 4) For 15%: find 10% then add half, 5) For 20%: divide by 5, 6) For 25%: divide by 4, 7) For 50%: divide by 2, 8) For 75%: multiply by 3 and divide by 4. Combine these for complex percentages: 35% = 30% + 5% = (3 x 10%) + (5%). Practice mental math with these shortcuts for exam speed.
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