📚 Percentages – PGECET Quantitative Aptitude Notes
PGECET (Post Graduate Entrance to Computer Engineering & Technology) focuses on fast, accurate calculations. Percentages appear in “Percentage & Ratio”, “Profit & Loss”, “Discounts”, “Interest” and “Compound Interest” questions. Mastering the basics will save time and reduce errors.
1️⃣ Simple Explanation
A percentage is a fractional part of 100.
- Percent sign (%) means “per one hundred”.
- To convert a decimal or fraction to a percentage, multiply by 100.
- To convert a percentage to a decimal, divide by 100.
Example
(0.45 \times 100 = 45%)
(25% = 0.25)
2️⃣ Key Points & Formulas
| Concept | Formula | Notes |
|---|---|---|
| Percentage of a number | ( \text{Part} = \frac{\text{Percent} \times \text{Whole}}{100} ) | Used for “what is 30% of 200?” |
| Finding the whole from a part | ( \text{Whole} = \frac{\text{Part} \times 100}{\text{Percent}} ) | “30% of a number is 60, find the number.” |
| Percentage increase | ( \text{New} = \text{Old} \times \left(1 + \frac{\text{Rate}}{100}\right) ) | Rate = % increase |
| Percentage decrease | ( \text{New} = \text{Old} \times \left(1 - \frac{\text{Rate}}{100}\right) ) | Rate = % decrease |
| Compound percentage (simple interest) | ( \text{Amount} = \text{Principal} \times \left(1 + \frac{r}{100}\right)^n ) | r = annual rate, n = years |
| Discount | ( \text{Discounted Price} = \text{List Price} \times \left(1 - \frac{d}{100}\right) ) | d = discount % |
| Profit/Loss | ( \text{Profit/Loss} = \text{Selling Price} - \text{Cost Price} ) %Profit = (\frac{\text{Profit}}{\text{Cost Price}}\times100) |
|
| Parts of a whole | Sum of parts = Whole. |
Quick Facts
| % | Equivalent decimal | Equivalent fraction |
|---|---|---|
| 1 % | 0.01 | 1/100 |
| 10 % | 0.10 | 1/10 |
| 25 % | 0.25 | 1/4 |
| 50 % | 0.50 | 1/2 |
| 75 % | 0.75 | 3/4 |
| 100 % | 1.00 | 1/1 |
3️⃣ Worked Example (PGECET style)
Question
A shopkeeper buys a batch of 200 kg of rice for ₹80 000. He sells it at a 15 % profit.
a) What is the selling price for the entire batch?
b) If he sells 50 % of the batch at the same profit, how much does he earn on that portion?
c) What would be his profit if he sold the remaining 50 % at 10 % profit instead?
Solution
Given
- Cost Price (CP) of 200 kg = ₹80 000
- Profit % on whole batch = 15 %
- Profit % on first half = 15 %
- Profit % on second half = 10 %
(a) Selling price of whole batch
[ \text{SP}_\text{whole} = CP \times \left(1 + \frac{15}{100}\right) = 80,000 \times 1.15 = ₹92,000 ]
(b) Profit on 50 % batch (100 kg)
Cost of 100 kg = (80,000 \times \frac{100}{200} = ₹40,000)
Selling price (15 % profit):
[ SP_{50%} = 40,000 \times 1.15 = ₹46,000 ]
Profit on that portion:
[ \text{Profit}_{50%} = 46,000 - 40,000 = ₹6,000 ]
(c) Profit on remaining 50 % at 10 % profit
Cost of 100 kg remains ₹40 000.
Selling price (10 % profit):
[ SP_{50%}^{10%} = 40,000 \times 1.10 = ₹44,000 ]
Profit:
[ \text{Profit}_{50%}^{10%} = 44,000 - 40,000 = ₹4,000 ]
Total profit = ₹6 000 + ₹4 000 = ₹10 000
Total selling price = ₹46 000 + ₹44 000 = ₹90 000
4️⃣ Quick Revision Summary
| Topic | Formula | Key Idea |
|---|---|---|
| % of a number | ( \text{Part} = \frac{P \times N}{100} ) | Find any portion of a whole. |
| Whole from % | ( N = \frac{\text{Part} \times 100}{P} ) | Reverse operation. |
| Increase/Decrease | ( \text{New} = N(1 \pm \frac{R}{100}) ) | + for increase, – for decrease. |
| Compound (interest, growth) | ( A = P \left(1 + \frac{r}{100}\right)^n ) | Exponential growth with compounding. |
| Discount | ( \text |