# Ratio, Proportion and Partnership — Simple Methods with Examples

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

A **ratio** compares two quantities of the same kind. If a class has 20 boys and 30 girls, boys : girls = 20 : 30 = **2 : 3**.

Think of a ratio as **parts**: for every 2 parts of boys there are 3 parts of girls.

## 1. The parts method

![₹500 split into 5 equal blocks of ₹100: A gets 2 blocks (₹200), B gets 3 blocks (₹300)](https://skills101.in/learn-img/aptitude/ratio-split.svg)

### Example 1
*Share ₹500 between A and B in the ratio 2 : 3.*

Total parts = 5. One part = 500 ÷ 5 = 100. A = 2 × 100 = **₹200**, B = **₹300**.

This one idea solves most ratio questions: **find the value of one part**.

### Example 2
*The ratio of boys to girls is 4 : 5. There are 36 boys. How many girls?*

4 parts = 36 → 1 part = 9 → girls = 5 × 9 = **45**.

## 2. Combining two ratios

*A : B = 2 : 3 and B : C = 4 : 5. Find A : B : C.*

B is in both. Make B the same: multiply the first by 4 and the second by 3.

- A : B = 8 : 12
- B : C = 12 : 15
- So A : B : C = **8 : 12 : 15**

## 3. Proportion

Four numbers a, b, c, d are **in proportion** if a : b = c : d, i.e. **a × d = b × c** ("product of extremes = product of means").

- **Mean proportional** of a and b = √(ab). Of 4 and 16 → √64 = **8**.
- **Third proportional** of a and b is c where a : b = b : c → c = b²/a. Of 4 and 6 → 36/4 = **9**.

### Example 3
*Find x if 3 : 5 = x : 40.*

3 × 40 = 5x → x = **24**.

## 4. Adding to a ratio

### Example 4
*Two numbers are in the ratio 3 : 5. If 9 is added to each, the ratio becomes 3 : 4. Find the numbers.*

Let them be 3k and 5k. (3k + 9)/(5k + 9) = 3/4 → 12k + 36 = 15k + 27 → k = 3. Numbers: **9 and 15**.

## 5. Coins

### Example 5
*A bag has ₹1, 50 p and 25 p coins in the ratio 1 : 2 : 4. The total value is ₹90. How many 25 p coins are there?*

Value per set of coins = 1 × ₹1 + 2 × ₹0.50 + 4 × ₹0.25 = 1 + 1 + 1 = ₹3. Number of sets = 90 ÷ 3 = 30. 25 p coins = 4 × 30 = **120**.

## 6. Partnership

Business profit is shared in the ratio of **money × time** each partner invested.

> **Profit share ∝ Investment × Time**

### Example 6
*A invests ₹40,000 for 12 months; B invests ₹60,000 for 6 months. The profit is ₹35,000. Find each share.*

- A: 40,000 × 12 = 4,80,000
- B: 60,000 × 6 = 3,60,000
- Ratio = 480 : 360 = 4 : 3 → total 7 parts → 1 part = 5,000
- A = **₹20,000**, B = **₹15,000**

### Example 7
*A starts a business with ₹50,000. After 4 months B joins with ₹75,000. What is the profit ratio after 1 year?*

A: 50,000 × 12 = 6,00,000. B: 75,000 × 8 = 6,00,000. Ratio = **1 : 1**.

## Common mistakes

- Forgetting to make the common term equal when combining ratios.
- In partnership, using only the investment and forgetting the **time**.
- Mixing units (₹ and paise, months and years). Convert first.

## Quick recap

- Ratio = parts. Find one part, then everything else.
- To combine A : B and B : C, make B equal.
- a : b = c : d ⇔ ad = bc. Mean proportional = √(ab).
- Partnership: share ∝ money × time.


Practice quiz and free certificate: https://skills101.in/learn/aptitude/ratio-and-proportion