Percentage Tricks for Fast Calculations and Shortcuts

Percentage Tricks use fraction conversions, base-100 calculations and simple algebraic rules to solve percentage questions quickly. This page covers percentage formulas, common fraction equivalents, successive percentage changes, profit and loss applications, and methods for calculating percentages mentally with fewer calculation steps.

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What Are Percentage Tricks?

Percentage tricks are shortcut methods for calculating a part, change or comparison as a fraction of 100. They use the formula percentage = (part ÷ whole) × 100 and equivalent fraction values for quick computation.

A percentage represents a quantity per 100. Thus, 25% means 25/100 or 1/4. In a statement such as 20% of 250, multiply 250 by 20/100: 250 × 20/100 = 50. The reference quantity, or base, must be identified before applying a percentage.

Percentage Tricks Formula & Tricks

Important Formulas

Basic Percentage Formula
Percentage = (Part ÷ Whole) × 100

Use this when the part and whole are given and the percentage is required.

Finding the Part
Part = (Percentage ÷ 100) × Whole

Use this to find a percentage of a known whole quantity.

Percentage Change
Percentage change = [(New value − Original value) ÷ Original value] × 100

A positive result indicates an increase, while a negative result indicates a decrease.

Successive Percentage Change
Net change = a + b + (ab ÷ 100)

Use positive values for successive increases and negative values for decreases. Here, a and b are the two percentage changes.

Percentage Difference
Percentage difference = [|A − B| ÷ ((A + B) ÷ 2)] × 100

Use this when two values are compared with their average as the reference.

Quick Tricks

Use 10%, 1% and 5% as building blocks

Find 10% by dividing by 10, 1% by dividing by 100 and 5% by taking half of 10%. Combine these values to calculate other percentages.

Example: 18% of 250 = 10% of 250 + 5% of 250 + 3% of 250 = 25 + 12.5 + 7.5 = 45.
Interchange the percentage and the number

For any two numbers, x% of y equals y% of x. Choose the form that produces an easier calculation.

Example: 16% of 25 = 25% of 16 = 4.
Convert percentages into familiar fractions

Use common equivalents such as 50% = 1/2, 25% = 1/4, 12.5% = 1/8 and 6.25% = 1/16.

Example: 12.5% of 640 = 640 ÷ 8 = 80.
Use the complement for percentages near 100%

To find 98% of a number, subtract 2% of it from the number. This is faster than multiplying by 98/100.

Example: 98% of 750 = 750 − 2% of 750 = 750 − 15 = 735.

Percentage Tricks Concepts

Percentage to Fraction and Decimal Conversion

To convert a percentage into a fraction, divide it by 100; to convert it into a decimal, move the decimal point two places left.

For example, 35% = 35/100 = 7/20 = 0.35. For a fraction or decimal converted into a percentage, multiply by 100. Thus, 3/8 = 0.375 = 37.5%.

Example: 62.5% = 62.5/100 = 5/8 = 0.625.

Common Percentage Equivalents

Common fraction equivalents reduce calculation time because the percentage can be applied through division or multiplication.

Useful values include 50% = 1/2, 33⅓% = 1/3, 25% = 1/4, 20% = 1/5, 12.5% = 1/8, 10% = 1/10, 6.25% = 1/16 and 4% = 1/25.

Example: 33⅓% of 270 = 270 ÷ 3 = 90.

The Interchange Rule for Percentages

The percentage of a number can be interchanged: x% of y = y% of x.

Algebraically, x% of y = (x/100) × y = (y/100) × x = y% of x. This rule is useful when one of the numbers has a convenient percentage form.

Example: 24% of 50 = 50% of 24 = 12.

Successive Percentage Increase and Decrease

Two successive percentage changes are not added directly unless the second change is calculated on the original base.

For changes of a% and b%, the net percentage change is a + b + ab/100, using a negative sign for a decrease. A 20% increase followed by a 10% decrease gives 20 − 10 − 2 = 8% net increase.

Example: An amount of 500 becomes 600 after a 20% increase and then 540 after a 10% decrease. The final increase is 40/500 × 100 = 8%.

Reverse Percentage Calculation

To find an original value after a percentage change, divide the final value by the corresponding multiplier.

After an increase of r%, Original value = Final value ÷ (1 + r/100). After a decrease of r%, Original value = Final value ÷ (1 − r/100). For example, if a price after a 20% increase is 720, its original value is 720 ÷ 1.2 = 600.

Example: A value after a 25% decrease is 450. Original value = 450 ÷ 0.75 = 600.

Percentage Tricks Video Lessons

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8 Lessons
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Percentage Tricks in Vedic Maths

Learn quick Vedic Maths techniques for calculating percentages efficiently, simplifying percentage-based operations, and improving speed and accuracy in quantitative aptitude problems.

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Practice Percentage Tricks Questions

Practise published questions related to this topic.

1The marked price of an article is ₹500. During a sale, its price is reduced to ₹450. What is the percentage decrease in price?→ 2A shopkeeper sold an article for ₹540 at a 10% loss. What was its cost price?→ 3A product is marked at ₹500 with a 20% discount. What is the selling price?→ 4Find the total numbers from 1 to 100 which are (i) exactly divisible by 4 and (ii) has at least 4 as a digit.→ 5A salesman marks his goods 75% above the cost price and gives a discount of 52% on them. Find the percentage of this gain or loss.→ 6Three numbers are in the ratio 11 : 3 : 2, and their LCM is 2706. Their HCF is:→ 7The cost price of an article is Rs. 15000. It is sold at a profit of 20 percent. A discount of 25 percent was given. What is the marked price of the article?→ 8A shirt is marked at ₹500. The shopkeeper first gives a 20% discount and then reduces the price further by ₹20. What is the selling price?→ 9During a sale, 40% of the goods are sold at a 44% profit, 25% of the remaining goods are sold at a 29% profit and the rest are sold at a 39% loss. If there is an overall profit of x%, then what is the value of x?→ 10An 11-digit number 8732326687X is divisible by 18. What is the value of X?→

Percentage Tricks Quick Quiz

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Quick Revision Notes

Percentage Tricks: Quick Revision Points

Remember these formulas, equivalents and calculation rules for fast percentage solving.

  • Percentage = (Part ÷ Whole) × 100.
  • Part = (Percentage ÷ 100) × Whole.
  • x% of y = y% of x.
  • 50% = 1/2, 25% = 1/4, 20% = 1/5, 12.5% = 1/8 and 6.25% = 1/16.
  • Successive changes: net change = a + b + ab/100, with decreases represented by negative values.
  • For an increase of r%, multiply the original value by 1 + r/100.
  • For a decrease of r%, multiply the original value by 1 − r/100.
  • To reverse an increase or decrease, divide the final value by its corresponding multiplier.

Percentage Tricks FAQs

What is the fastest way to calculate 15% of a number?

Find 10% and 5%, then add them. For example, 15% of 240 = 24 + 12 = 36.

How do you calculate a percentage increase?

Use [(New value − Original value) ÷ Original value] × 100. If a value rises from 400 to 460, the increase is 60/400 × 100 = 15%.

What is the result of a 20% increase followed by a 20% decrease?

The net change is 20 − 20 − (20 × 20)/100 = −4%. For an original value of 100, the final value is 96.

How do you find the original value after a 30% discount?

Divide the final price by 0.70 because the discounted price is 70% of the original. If the final price is 840, the original price is 840 ÷ 0.70 = 1,200.

Why is 25% of 80 equal to 80% of 25?

Because x% of y = y% of x. Both calculations equal 20: 25/100 × 80 = 80/100 × 25 = 20.

How do you calculate 37.5% mentally?

Convert 37.5% to 3/8. Therefore, 37.5% of 320 = 320 × 3/8 = 120.

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