Mathematics Short Tricks/ MATH PERCENTAGE

June 6, 2025June 7, 2025 Diznr International 0 Comments

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Mathematics Short Tricks – Percentage

Percentages are one of the most important topics in competitive exams like SSC, Banking, GATE, CAT, etc. Here are some quick tricks & formulas to solve percentage problems FAST!

Basic Percentage Formula

$Value)×100\text{Percentage} = \left(\frac{\text{Value}}{\text{Total Value}}\right) \times 100$

Example: If a student scores 45 marks out of 60, what is the percentage?

$(4560)×100=75%\left(\frac{45}{60}\right) \times 100 = 75\%$

Fast Conversion Between Fractions & Percentages

Memorizing common fraction-percentage conversions will save time!

Fraction	Percentage
1/2	50%
1/3	33.33%
1/4	25%
1/5	20%
1/6	16.66%
1/7	14.28%
1/8	12.5%
1/9	11.11%
1/10	10%

Example Trick: If you see 1/5, immediately think 20%!

Percentage Increase/Decrease Formula

$Value)×100\text{Increase/Decrease} = \left(\frac{\text{Change in Value}}{\text{Original Value}}\right) \times 100$

Example: If the price of a mobile increases from ₹2000 to ₹2500, what is the percentage increase?

$(2500−20002000)×100=(5002000)×100=25%\left(\frac{2500 – 2000}{2000}\right) \times 100 = \left(\frac{500}{2000}\right) \times 100 = 25\%$

Shortcut Trick:

If a value increases by “x%”, the new value =

$Value×(1+x100)\text{Old Value} \times \left(1 + \frac{x}{100}\right)$

If a value decreases by “x%”, the new value =

$Value×(1−x100)\text{Old Value} \times \left(1 – \frac{x}{100}\right)$

Example: If a ₹500 product increases by 20%, the new price =

$500 \times \left(1 + \frac{20}{100}\right) = 500 \times 1.2 = 600$

Successive Percentage Change Formula

When two percentage changes happen successively, use:

$Change=x+y+xy100\text{Total Percentage Change} = x + y + \frac{xy}{100}$

Example: A price first increases by 20%, then decreases by 10%. What is the net change?

$\frac{(20 \times -10)}{100} = 20 – 10 – 2 = 8\%$

Final answer: 8% increase

Finding Population Growth or Depreciation

If the population increases/decreases by r% per year, the population after n years is:

$P_0 \times \left(1 + \frac{r}{100}\right)^n$

Example: If a town has 10,000 people and grows by 5% per year, what will be the population after 3 years?

$\times \left(1 + \frac{5}{100}\right)^3$ $\times (1.157) = 11,570$

Final Answer: 11,570 people

Fastest Way to Find % of Any Number (Vedic Trick)

Trick for Finding 10%, 5%, 1% Fast

10% of a number → Move one decimal left.
5% of a number → Take half of 10%.
1% of a number → Move two decimals left.

Example: Find 7% of 320.
1% of 320 = 3.2
7% = 3.2 × 7 = 22.4

Done in seconds without a calculator!

Shortcut for Percentage to Ratio Conversion

Formula:

$Denominator×100\text{Percentage} = \frac{\text{Ratio Numerator}}{\text{Ratio Denominator}} \times 100$

Examples:

75% = 3:4
80% = 4:5
25% = 1:4
40% = 2:5

Quick Trick: Always convert x% to x/100, then reduce the fraction.

Reverse Percentage Trick

If x% of a number is y, then the original number is:

$y×100x\frac{y \times 100}{x}$

Example: 30% of a number is 90. What is the number?

$90×10030=300\frac{90 \times 100}{30} = 300$

Final Answer: 300

Summary of Tricks

Memorize fraction-percentage conversions
Use formulas for percentage increase/decrease
Apply successive % formula for multiple changes
Use Vedic Math tricks for quick calculations
Convert percentage to ratio and vice versa easily

Master these tricks and solve any percentage question in seconds!

Would you like practice questions or PDFs for revision?

Quick Percentage Calculation Tricks

The 1% Method:
- To find 1% of any number, move the decimal point two places to the left.
- Example: 1% of 250 = 2.5
- To find 17% of 250:
  - 1% of 250 = 2.5
  - 17 × 2.5 = 42.5
The 10% Rule:
- To find 10% of a number, move the decimal point one place to the left.
- Example: 10% of 80 = 8(StudyPug, BYJU’S)
Doubling and Halving:
- To find 20% of a number, double the 10% value.
- Example: 10% of 150 = 15; 20% = 15 × 2 = 30
- To find 5%, halve the 10% value.
- Example: 10% of 200 = 20; 5% = 20 ÷ 2 = 10
Swapping Percentage and Base:
- Sometimes, swapping the percentage and the base makes calculation easier.
- Example: 8% of 25 = 25% of 8 = 2(Reddit)
Percentage Increase/Decrease:
- To calculate percentage change:
  - Percentage Change = ((New Value – Original Value) / Original Value) × 100
- Example: Price increases from $50 to $60:
  - ((60 – 50) / 50) × 100 = 20% increase
Fraction to Percentage Conversion:
- Memorize common fraction-percentage equivalents:
  - 1/2 = 50%
  - 1/3 ≈ 33.33%
  - 1/4 = 25%
  - 1/5 = 20%
  - 1/6 ≈ 16.66%
  - 1/8 = 12.5%
  - 1/10 = 10%

Additional Resources

For more in-depth explanations and examples, consider exploring the following resources:

GeeksforGeeks: Maths Trick to Find Percentage
PrepInsta: Tips and Tricks and Shortcuts of Percentage
StudyPug: Master Percent of a Number

DIZNR INTERNATIONAL

Mathematics Short Tricks/ MATH PERCENTAGE

Mathematics Short Tricks – Percentage

Basic Percentage Formula

Fast Conversion Between Fractions & Percentages

Percentage Increase/Decrease Formula

Shortcut Trick:

Successive Percentage Change Formula

Finding Population Growth or Depreciation

Fastest Way to Find % of Any Number (Vedic Trick)

Trick for Finding 10%, 5%, 1% Fast

Shortcut for Percentage to Ratio Conversion

Reverse Percentage Trick

Summary of Tricks

QUALITATIVE APTITUDE TRICKS & SHORTCUTS FOR