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Mathematics Short Tricks/ MATH PERCENTAGE

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Mathematics Short Tricks/ MATH PERCENTAGE

https://www.gyanodhan.com/video/5A3.%20Mathematics%20Short%20Tricks/153.%20MATH%20PERCENTAGE.mp4

 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

Percentage=(ValueTotal 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

Increase/Decrease=(Change in ValueOriginal 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 =

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

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

Old 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×(1+20100)=500×1.2=600500 \times \left(1 + \frac{20}{100}\right) = 500 \times 1.2 = 600

 Successive Percentage Change Formula

When two percentage changes happen successively, use:

Total Percentage 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?

20+(−10)+(20×−10)100=20−10−2=8%20 + (-10) + \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=P0×(1+r100)nP = 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?

P=10000×(1+5100)3P = 10000 \times \left(1 + \frac{5}{100}\right)^3 =10000×(1.157)=11,570= 10000 \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:

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

Examples:

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?

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