Percentages: Concepts and Formulas for Placement Aptitude Tests

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Percentages is one of the fundamental topics for placement aptitude tests. Here are some quick concepts and formulas to remember

  1. Any percentage can be expressed as a decimal by dividing the percentage figure by 100

Q: How will you express 5% in decimal?

Sol: 5% = 5/100 = 0.05

2. Percentage change = (Absolute value change/ Original Qty) * 100

Q: Lara earned $1,500 last month and $1,200 this month. What is the percentage decrease in her earnings?

Sol: Percentage change = (1,500 - 1,200) ÷ 1,500 × 100 = 20%

3. If the percentage increase is p%, then the new value is = Original value * ( 1 + p/100)

Q: A shirt costs $40 and the price increased by 15%. What is the new price of the shirt?

Sol : New price = 40 × (1 + 15/100) = 46

4. If the new value is “k” times the old value, then the percentage increase = (k-1)*100

Q: A city’s population doubled in 10 years. What is the percentage increase?

Sol: Percentage increase = (2 - 1) × 100 = 100%

5. If an item’s value goes up by x%, the percentage reduction to be now made to bring it back to the original level is = [100x/(100+x)]%

Q: A car's price went up by 25% to $25,000. What percentage discount is needed to bring it back to the original price?

Sol: Percentage discount = (100 × 25) ÷ (100 + 25) = 20%

6. For successive changes of p%, q% and r%, the effective percentage increase = [(1+p/100)(1+q/100)(1+r/100)] — 1] * 100%

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