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The percentage expression “After a 15 percent decrease, a value becomes 208.25. What was the original value” is evaluated with Original value = final value ÷ (1 − rate)., producing 245.0 as the option-specific result.
Solving “After a 15 percent decrease, a value becomes 208.25. What was the original value” requires the relationship Original value = final value ÷ (1 − rate).; substituting the stated quantities gives 208.25 ÷ 0.85 = 245.; hence 245.0 is the calculated result and option D is correct.
FAQ
Common questions and clear answers for this topic.
The answer is 245.0. Using Original value = final value ÷ (1 − rate), 208.25 ÷ 0.85 = 245.
Original value = final value ÷ (1 − rate)
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.
