Percentage
Overview
Percentage is one of the most fundamental and frequently tested topics in SBI Clerk Prelims. It forms the foundation for several other arithmetic topics including Profit and Loss, Simple and Compound Interest, Data Interpretation, and Ratio problems. You cannot afford to be slow or inaccurate here.
In the exam, percentage questions appear both as direct calculation problems in the Simplification/Approximation section and as applied concepts within DI sets. Mastery means two things: knowing the fraction-to-percentage conversions by heart, and being able to quickly compute percentage change in either direction. Speed is everything—most percentage problems should take under 30 seconds.
The key skill is mental calculation. Memorize common percentage-fraction equivalents and practice computing 10%, 5%, 1% of any number instantly. This forms your calculation base for deriving any percentage quickly.
Key Concepts
- Percentage means "per hundred": x% = x/100. Converting between fractions, decimals, and percentages must be instantaneous.
- Percentage of a number: x% of N = (x × N)/100. Always compute 10% first, then build up or down.
- Percentage change formula: Change% = (Difference / Original) × 100. The denominator is always the original value, not the new value.
- Successive percentage changes: Two changes of a% and b% give net change = a + b + (ab/100). This avoids multi-step calculation.
- Percentage increase vs decrease reversal: A p% increase followed by reversal requires a decrease of [100p/(100+p)]%, not p%.
- Population/Depreciation formula: Final = Initial × (1 ± r/100)^n, where n is time periods and r is rate per period.
- Fraction-Percentage equivalents are non-negotiable: 1/2 = 50%, 1/3 ≈ 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 ≈ 16.67%, 1/8 = 12.5%, 1/9 ≈ 11.11%.
Formulas / Key Facts
| Formula | Context |
|---|---|
| x% of N = (x × N)/100 | Finding percentage of any number |
| Percentage Change = [(New − Old)/Old] × 100 | Increase or decrease calculation |
| Net change for a% and b% = a + b + ab/100 | Successive percentage changes |
| If A is x% more than B, then B is [100x/(100+x)]% less than A | Reversal problems |
| If A is x% less than B, then B is [100x/(100−x)]% more than A | Reversal problems |
| Final = Initial × (1 + r/100)^n | Compound growth (population, price) |
| Final = Initial × (1 − r/100)^n | Compound depreciation |
Must-memorize conversions:
- 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%
- 1/6 = 16.67%, 1/7 = 14.28%, 1/8 = 12.5%, 1/9 = 11.11%, 1/10 = 10%
- 1/11 = 9.09%, 1/12 = 8.33%, 1/15 = 6.67%, 1/20 = 5%
Worked Examples
Example 1: Basic percentage of a number
Find 35% of 1200.
Step 1: 10% of 1200 = 120 Step 2: 30% = 3 × 120 = 360 Step 3: 5% = half of 10% = 60 Step 4: 35% = 360 + 60 = 420
Example 2: Percentage change
A product's price increased from ₹450 to ₹540. Find the percentage increase.
Difference = 540 − 450 = 90 Percentage increase = (90/450) × 100 = (1/5) × 100 = 20%
Example 3: Successive percentage change
A shopkeeper increases price by 20% and then gives a 10% discount. What is the net percentage change in price?
Using formula: Net change = a + b + ab/100 Here a = +20, b = −10 Net change = 20 + (−10) + (20 × −10)/100 Net change = 20 − 10 − 2 = +8% (increase)
Example 4: Reversal percentage
If A's salary is 25% more than B's salary, by what percentage is B's salary less than A's?
Using formula: Required % = 100x/(100+x) = (100 × 25)/(100 + 25) = 2500/125 = 20%
Example 5: Population growth
The population of a town is 50,000. It increases by 10% in the first year and 20% in the second year. Find the population after 2 years.
After Year 1: 50,000 × 1.10 = 55,000 After Year 2: 55,000 × 1.20 = 66,000
Alternative: 50,000 × 1.10 × 1.20 = 50,000 × 1.32 = 66,000
Common Mistakes
- Using final value as base for percentage change → Always use the original value as denominator. If price goes from 80 to 100, increase = 20/80 = 25%, not 20/100 = 20%.
- Assuming successive equal changes cancel out → A 20% increase followed by 20% decrease does NOT return to original. Net effect = 20 + (−20) + (20 × −20)/100 = −4%. There's always a net loss.
- Confusing "more than" with "of" → "A is 25% more than B" means A = 1.25B. "A is 25% of B" means A = 0.25B. Read carefully.
- Reversing percentage incorrectly → If A is 20% more than B, students often say B is 20% less than A. Wrong. B is 100×20/120 = 16.67% less than A.
- Not simplifying fractions first → Calculate 45/300 as 45/300 = 3/20 = 15%, not by dividing decimals. Fraction simplification saves time.
Quick Reference
- 10% of any number: Move decimal one place left
- Successive changes: a + b + ab/100 (watch signs carefully)
- x% more → reverse is [100x/(100+x)]% less
- x% less → reverse is [100x/(100−x)]% more
- 25% = 1/4, 33.33% = 1/3, 12.5% = 1/8, 16.67% = 1/6
- Always base percentage change on the ORIGINAL value