Percentage
SSC-CGL Exams
1. Introduction
The percentage concept is the backbone of topics like profit & loss, simple interest, and data interpretation. It helps us express comparisons and ratios in a simple form — "out of 100." Let's master it with concepts, tricks, and SSC-style questions.
2. Concept of Percentage
Definition
Percentage means "per hundred."
Percentage = (Value / Total Value) × 100
Example
If a student scores 60 marks out of 80:
Percentage = (60/80) × 100 = 75%
3. Fraction–Percentage Conversion Table
| Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
| 1/2 | 50% | 1/8 | 12.5% |
| 1/3 | 33⅓% | 3/8 | 37.5% |
| 1/4 | 25% | 5/8 | 62.5% |
| 1/5 | 20% | 7/8 | 87.5% |
| 1/6 | 16⅔% | 1/9 | 11.11% |
| 1/7 | 14.28% | 1/10 | 10% |
| 2/3 | 66⅔% | 3/4 | 75% |
| 5/6 | 83⅓% | 9/10 | 90% |
Trick
To convert fraction → %, multiply by 100
To convert % → fraction, divide by 100
4. Successive Percentage Changes
When a value changes twice (increase/decrease), apply the Successive Change Formula:
Net % change = A + B + (AB/100)
where A and B are the two successive % changes. (Use negative sign for decrease.)
Example 1
Price of a pen increases by 10% and then again by 20%. Find the net percentage increase.
= 10 + 20 + (10×20)/100 = 32%
Answer: 32% increase
Example 2
A price increases by 20% and then decreases by 20%.
= 20 - 20 + (20×(-20))/100 = -4%
Answer: 4% decrease (final price decreases)
Example 3
If a student's marks increase by 25% and then by 10%, find the total increase.
= 25 + 10 + (25×10)/100 = 37.5%
Answer: 37.5% increase
5. Percentage Change Formula (General Use)
Percentage Change = (Change in Value / Original Value) × 100
Example
Population of a town rises from 20,000 to 25,000.
Increase % = (5000/20000) × 100 = 25%
6. Practice Problems
Q1. What percent is 45 of 150?
View Answer
(45/150) × 100 = 30%
Q2. Convert the following:
(a) 3/5 to percentage
(b) 60% to fraction
View Answer
(a) 3/5 × 100 = 60%
(b) 60/100 = 3/5
Q3. A number increases by 25% and then decreases by 25%. What is the net change?
View Answer
= 25 - 25 + (25×-25)/100 = -6.25%
So, net 6.25% decrease
Q4. Ram got 720 marks out of 900. What percent did he score?
View Answer
(720/900) × 100 = 80%
Q5. Price of sugar increased by 15% and then decreased by 10%. Find the net % change.
View Answer
= 15 - 10 + (15×-10)/100 = 3.5%
Net increase = 3.5%
Q6. If a man spends 85% of his income and saves ₹900, find his total income.
View Answer
Saving = 15%
So, 15% = ₹900 ⇒ 1% = ₹60 ⇒ 100% = ₹6000
Income = ₹6000
Q7. In a college, number of girls increased from 400 to 480. Find the % increase.
View Answer
(80/400) × 100 = 20%
20% increase
7. Quick Recap
| Concept | Formula / Trick |
|---|---|
| Percentage | (Value / Total) × 100 |
| Fraction → % | Multiply by 100 |
| % → Fraction | Divide by 100 |
| Successive % | A + B + (AB/100) |
| Increase/Decrease | (Change / Original) × 100 |
You've completed Article 2: Percentage!
Courage Tip: Always connect percentages with fractions mentally — it helps in fast calculations and boosts accuracy in DI, Profit & Loss, and SI/CI topics.
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