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Quantitative Aptitude
hardQ. No. 5221-a-number-increases-by-20-percent-and-then-decreases-by-20-percent-what-is-the-final-value-if-the

A number increases by 20 percent and then decreases by 20 percent. What is the final value if the original number was 313?

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The percentage expression “A number increases by 20 percent and then decreases by 20 percent. What is the final value if the original number was 313” is evaluated with Final value = original × (1 + increase rate) × (1 − decrease rate)., producing 300.48 as the option-specific result.

A300.48
B265.48
C338.48
D329.48
Correct Answer: 300.48Your Answer: A

Explanation

Solving “A number increases by 20 percent and then decreases by 20 percent. What is the final value if the original number was 313” requires the relationship Final value = original × (1 + increase rate) × (1 − decrease rate).; substituting the stated quantities gives 313 × 1.2 × 0.8 = 300.48.; hence 300.48 is the calculated result and option A is correct.

Important Notes

  • Method for “A number increases by 20 percent and then decreases by 20 percent. What is the final value if the original number was 313”: use Final value = original × (1 + increase rate) × (1 − decrease rate)..
  • Substitution for “A number increases by 20 percent and then decreases by 20 percent. What is the final value if the original number was 313” produces 313 × 1.2 × 0.8 = 300.48..
  • Verification for “A number increases by 20 percent and then decreases by 20 percent. What is the final value if the original number was 313”: 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 20%. What is the final value if the original number was 313?

The answer is 300.48. Using Final value = original × (1 + increase rate) × (1 − decrease rate), 313 × 1.2 × 0.8 = 300.48.

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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