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Quantitative Aptitude
mediumQ. No. 6772-a-number-increases-by-20-percent-and-then-decreases-by-10-percent-if-the-original-number-was-461

A number increases by 20 percent and then decreases by 10 percent. If the original number was 461, what is the final value?

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The percentage expression “A number increases by 20 percent and then decreases by 10 percent. If the original number was 461, what is the final value” is evaluated with Final value = original × (1 + increase rate) × (1 − decrease rate)., producing 497.88 as the option-specific result.

A532.88
B588.88
C435.88
D497.88
Correct Answer: 497.88Your Answer: D

Explanation

Solving “A number increases by 20 percent and then decreases by 10 percent. If the original number was 461, what is the final value” requires the relationship Final value = original × (1 + increase rate) × (1 − decrease rate).; substituting the stated quantities gives 461 × 1.2 × 0.9 = 497.88.; hence 497.88 is the calculated result and option D is correct.

Important Notes

  • Method for “A number increases by 20 percent and then decreases by 10 percent. If the original number was 461, what is the final value”: use Final value = original × (1 + increase rate) × (1 − decrease rate)..
  • Substitution for “A number increases by 20 percent and then decreases by 10 percent. If the original number was 461, what is the final value” produces 461 × 1.2 × 0.9 = 497.88..
  • Calculated answer for “A number increases by 20 percent and then decreases by 10 percent. If the original number was 461, what is the final value” is 497.88, matching option D.
  • Verification for “A number increases by 20 percent and then decreases by 10 percent. If the original number was 461, what is the final value”: retain the stated base quantity throughout the percentage calculation.

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Percentage FAQs

Common questions and clear answers for this topic.

A number increases by 20% and then decreases by 10%. If the original number was 461, what is the final value?

The answer is 497.88. Using Final value = original × (1 + increase rate) × (1 − decrease rate), 461 × 1.2 × 0.9 = 497.88.

Which formula is used?

Final value = original × (1 + increase rate) × (1 − decrease rate)

What is Percentage and how is it used in competitive exam problems?

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.

What are the important percentage-fraction equivalents to memorize?

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.

How to calculate Percentage Increase and Decrease?

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.

How to solve population growth problems using percentage?

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.

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