# Percentages — Shortcuts, Successive Change and Exam Questions

Source: https://skills101.in/learn/aptitude/percentages — Skills101 free tutorial (Quantitative Aptitude). Updated 2026-11-09.

**Per cent** means "out of 100". 35% means 35 out of every 100, or 35/100.

Percentages are the **most important** aptitude topic: profit & loss, interest, data interpretation and even probability questions use them.

## 1. Fractions you must know as percentages

![Table of common fractions and their percentages: 1/2 = 50%, 1/3 = 33.33%, 1/8 = 12.5% and more](https://skills101.in/learn-img/aptitude/percent-fractions.svg)

These turn hard percentages into easy fractions:

- 12.5% of 640 = ⅛ of 640 = **80**
- 16.67% of 360 = ⅙ of 360 = **60**
- 37.5% = ⅜, 62.5% = ⅝, 87.5% = ⅞

> **Trick:** x% of y = y% of x. So 16% of 25 = 25% of 16 = **4**.

## 2. Percentage change

> **% change = (change ÷ original) × 100**

Always divide by the **original** (old) value.

### Example 1
*A phone's price went from ₹12,000 to ₹15,000. What is the % increase?*

Change = 3,000. % increase = 3000 ÷ 12000 × 100 = **25%**.

## 3. Increase or decrease by a percentage — use a multiplier

- Increase by 20% → multiply by **1.20**
- Decrease by 15% → multiply by **0.85**

### Example 2
*A town's population is 50,000 and grows 10% every year. What is it after 2 years?*

50,000 × 1.1 × 1.1 = **60,500**.

## 4. Successive percentage change

When one change happens **after** another, they do not simply add.

![Bars: ₹100 goes up 20% to ₹120, then down 20% to ₹96 — a net loss of 4%](https://skills101.in/learn-img/aptitude/successive-change.svg)

> **Net change for a% then b% = a + b + (a × b)/100**
> (use a negative sign for a decrease)

- +20% then −20% → 20 − 20 − 400/100 = **−4%**
- +10% then +10% → 10 + 10 + 100/100 = **+21%**

### Example 3
*A shirt's price is raised by 25% and then reduced by 20%. What is the net change?*

25 − 20 + (25 × −20)/100 = 5 − 5 = **0%**. The price is back where it started.

## 5. "By how much less?" — the reverse question

If A is r% **more** than B, then B is less than A by:

> **r ÷ (100 + r) × 100 %**

### Example 4
*Ravi's salary is 25% more than Amit's. By what % is Amit's salary less than Ravi's?*

25 ÷ 125 × 100 = **20%**.

(Check with numbers: Amit = 100, Ravi = 125. Amit is 25 less than 125 → 25/125 = 20% ✓)

Similarly, if A is r% **less** than B, B is more than A by r ÷ (100 − r) × 100 %.

## 6. Price up, so use less — expenditure stays the same

### Example 5
*Petrol becomes 25% costlier. By what % should a family cut its usage so the monthly bill does not change?*

Same formula: 25 ÷ 125 × 100 = **20%**.

## 7. Working back to the original

### Example 6
*After spending 30% of her salary on rent and 20% on food, Priya has ₹20,000 left. What is her salary?*

She spends 30 + 20 = 50%, so 50% of salary = 20,000 → salary = **₹40,000**.

### Example 7
*In an exam, a student got 35% and failed by 15 marks. The pass mark is 260. What are the maximum marks?*

35% of max = 260 − 15 = 245 → max = 245 ÷ 0.35 = **700**.

## Common mistakes

- Dividing by the **new** value in % change. Always divide by the **original**.
- Adding successive changes (20% up and 20% down is **not** 0%).
- Thinking "A is 25% more than B" means "B is 25% less than A". It is 20%.

## Quick recap

- Learn the fraction table: ⅛ = 12.5%, ⅙ = 16.67%, etc.
- % change = change ÷ original × 100.
- Use multipliers: +20% → × 1.2, −15% → × 0.85.
- Successive: a + b + ab/100.
- "How much less": r/(100 + r) × 100.


Practice quiz and free certificate: https://skills101.in/learn/aptitude/percentages