📊 Percentages – Quick Study Notes
Target Audience: Jharkhand Police Constable (JPC) – Quantitative Aptitude
Length: ~2 pages (easy to read on a phone or print)
1️⃣ Simple Explanation
A percentage is a way of expressing a fraction of 100.
- Formula:
[ \text{Percentage} = \frac{\text{Part}}{\text{Whole}}\times 100 ] - If you know the percentage and the whole, you can find the part (or “amount”).
- If you know the part and the whole, you can find the percentage.
- If you know the part and the percentage, you can find the whole.
2️⃣ Key Points to Remember
| Scenario | What you know | What you need to find | Formula (in words) |
|---|---|---|---|
| Find % | Part & Whole | % | ((\text{Part}/\text{Whole}) \times 100) |
| Find Part | % & Whole | Part | ((\text{Percentage} \times \text{Whole}) / 100) |
| Find Whole | Part & % | Whole | ((\text{Part} \times 100) / \text{Percentage}) |
| Increase/Decrease | Original value & % change | New value | (\text{New} = \text{Original} \pm (\text{Original} \times \text{Rate}/100)) |
| Compound increase | Current value & % increase | New value | (\text{New} = \text{Current} \times (1 + \text{Rate}/100)) |
Quick Tips
- Convert percentages to decimals: 25 % → 0.25.
- Use “×100” or “÷100” only once in each problem; combine with multiplication or division to keep it neat.
- Check units: “%” always means “per hundred”.
3️⃣ Worked Example
Problem
A police academy has 120 cadets. 30 % of them are female.
- a) How many female cadets are there?
- b) If 15 % of the female cadets get a special award, how many cadets receive the award?
Solution
(a) Number of female cadets
[ \text{Female} = \frac{30}{100} \times 120 = 0.30 \times 120 = 36 ] Answer: 36 female cadets.
(b) Cadets receiving the award
First find 15 % of the 36 female cadets:
[
\text{Awardees} = \frac{15}{100} \times 36 = 0.15 \times 36 = 5.4
]
Since we cannot have a fraction of a cadet, round appropriately (usually to the nearest whole number).
Answer: 5 cadets receive the award (if fractional, clarify rounding rule).
4️⃣ Quick Revision Summary
| Question | What you should do? | Quick formula |
|---|---|---|
| Find % of a number | Multiply the number by the percentage, then divide by 100 | ((\text{Number} \times \text{Percent})/100) |
| Find part from % | Multiply whole by percentage, divide by 100 | ((\text{Whole} \times \text{Percent})/100) |
| Find whole from % | Multiply part by 100, divide by percentage | ((\text{Part} \times 100)/\text{Percent}) |
| Apply increase/decrease | Add/subtract (original × rate/100) | (\text{New} = \text{Old} \pm (\text{Old} \times \text{Rate}/100)) |
| Compound change | Multiply by (1 + rate/100) | (\text{New} = \text{Old} \times (1+\text{Rate}/100)) |
Practice Tip:
- Convert all percentages to decimals first.
- Work step‑by‑step; write each intermediate step.
- Double‑check with a quick mental estimate (e.g., 20 % of 100 is 20, so 20 % of 200 should be ~40).
Good luck, Constable! 🚓
Keep practicing with varied problems; the key is to become comfortable moving between the three forms: part, whole, and percentage.