📚 JNU Entrance – Quantitative Aptitude
Topic: Percentages
What is a percentage?
A percentage is just a way to say “out of 100.”
Think of a pizza cut into 100 slices; each slice is 1 %.
So, if you eat 25 slices, you’ve eaten 25 % of the pizza.
1️⃣ Converting Between Forms
| What you start with | What you want | How to do it |
|---|---|---|
| Whole number (e.g., 25) | Percent (e.g., 25 %) | x % = x |
| Percent (e.g., 25 %) | Whole number | x = x ÷ 100 |
| Decimal (e.g., 0.25) | Percent | x % = x × 100 |
| Percent (e.g., 25 %) | Decimal | x = x ÷ 100 |
Tiny Example
- 40 % →
40 ÷ 100 = 0.40 - 0.15 →
0.15 × 100 = 15 %
2️⃣ Finding a Percentage of a Number
Formula
Part = Whole × (Percent ÷ 100)
Steps
- Convert the percent to a decimal (
% ÷ 100). - Multiply that decimal by the whole number.
Tiny Example
- What is 30 % of 200?
30 % → 0.30
200 × 0.30 = 60
→ 60 is 30 % of 200.
3️⃣ Finding the Whole When a Part and Percent Are Known
Formula
Whole = Part ÷ (Percent ÷ 100)
Tiny Example
- If 40 is 20 % of a number, what is the number?
20 % → 0.20
40 ÷ 0.20 = 200
→ The whole number is 200.
4️⃣ Percentage Increase / Decrease
| Situation | Formula | Tiny Example |
|---|---|---|
| Increase | New = Old × (1 + Percent ÷ 100) |
20 % increase on 50 → 50 × (1 + 0.20) = 60 |
| Decrease | New = Old × (1 – Percent ÷ 100) |
15 % decrease on 80 → 80 × (1 – 0.15) = 68 |
Analogy – Think of a price tag that goes up or down.
5️⃣ Two‑Way Percentage (Both Ways)
Suppose a number grows by 10 % and then shrinks by 10 %.
The final number is not the same as the original.
Why?
- First, you add 10 %:
Old × 1.10. - Then you take 10 % off that new amount:
(Old × 1.10) × 0.90 = Old × 0.99.
So you lose 1 % overall.
Tiny Example
- Start with 100.
10 % up → 110.
10 % down → 99.
→ Final = 99, not 100.
6️⃣ Percentage Change (What It Is)
Percentage Change = ((New – Old) ÷ Old) × 100
Tiny Example
- Old = 50, New = 65.
((65 – 50) ÷ 50) × 100 = 15 ÷ 50 × 100 = 30 %
→ The value grew by 30 %.
7️⃣ Quick Tips for JNU Entrance
| Tip | What to Remember |
|---|---|
| Read the question carefully | Does it ask for a part, whole, or change? |
| Convert to decimals early | It keeps the math simple. |
| Work backward when needed | If you know the part and the percent, find the whole. |
| Check units | 10 % of 200 ₹ = ₹20, not ₹200. |
| Practice with real numbers | Use money, time, or distances—anything you encounter daily. |
8️⃣ Mini Practice Set
| # | Question | Quick Work‑Through |
|---|---|---|
| 1 | What is 25 % of 80? | 0.25 × 80 = 20 |
| 2 | 60 is 15 % of what? | 60 ÷ 0.15 = 400 |
| 3 | A price increases from 120 ₹ to 150 ₹. What is the percent increase? | ((150‑120) ÷ 120) × 100 = 25 % |
| 4 | A number grows by 12 % and then shrinks by 12 %. What is the net change? | 1.12 × 0.88 = 0.9856 → –1.44 % |
🎯 Summary
- Percent = “out of 100.”
- Convert to decimals for easy multiplication/division.
- Use simple formulas for part, whole, increase, or decrease.
- Remember that two‑way changes don’t cancel out.
- Practice with everyday numbers to get comfortable.
Good luck with your JNU Entrance preparation! 🚀