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Quantitative Aptitude
mediumQ. No. 6188-a-number-increases-by-20-percent-and-then-decreases-by-5-percent-if-the-original-number-was-414

A number increases by 20 percent and then decreases by 5 percent. If the original number was 414, what is the final value?

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The percentage expression “A number increases by 20 percent and then decreases by 5 percent. If the original number was 414, what is the final value” is evaluated with Final value = original × (1 + increase rate) × (1 − decrease rate)., producing 471.96 as the option-specific result.

A540.96
B432.96
C471.96
D414.96
Correct Answer: 471.96Your Answer: C

Explanation

Solving “A number increases by 20 percent and then decreases by 5 percent. If the original number was 414, what is the final value” requires the relationship Final value = original × (1 + increase rate) × (1 − decrease rate).; substituting the stated quantities gives 414 × 1.2 × 0.95 = 471.96.; hence 471.96 is the calculated result and option C is correct.

Important Notes

  • Method for “A number increases by 20 percent and then decreases by 5 percent. If the original number was 414, 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 5 percent. If the original number was 414, what is the final value” produces 414 × 1.2 × 0.95 = 471.96..
  • Calculated answer for “A number increases by 20 percent and then decreases by 5 percent. If the original number was 414, what is the final value” is 471.96, matching option C.
  • Verification for “A number increases by 20 percent and then decreases by 5 percent. If the original number was 414, 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 5%. If the original number was 414, what is the final value?

The answer is 471.96. Using Final value = original × (1 + increase rate) × (1 − decrease rate), 414 × 1.2 × 0.95 = 471.96.

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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