**TOPIC 9: RATIO, PROFIT AND LOSS**

**Ratio**

A ratio – is a way of comparing quantities measured in the same units

Examples of ratios

- A class has 45 girls and 40 boys. The ratio of number of boys to the number of girls = 40: 45
- A football ground 100 𝑚 long and 50 𝑚 wide. The ratio of length to the width = 100: 50

**NOTE:**Ratios can be simplified like fractions

- 40: 45 = 8: 9
- 100: 50 = 2: 1

A Ratio in its Simplest Form

Express a ratio in its simplest form

Example 1

Simplify the following ratios, giving answers as whole numbers

Solution

A Given Quantity into Proportional Parts

Divide a given quantity into proportional parts

Example 2

Express the following ratios in the form of

**Solution**

To increase or decrease a certain quantity in a given ratio, multiply the quantity with that ratio

Example 3

- Increase 6 𝑚 in the ratio 4 ∶ 3
- Decrease 800 /− in the ratio 4 ∶ 5

Solution

**Profits and Loss**

Profit or Loss

Find profit or loss

If you buy something and then sell it at a higher price, then you have a profit which is given by: Profit = selling price − buying price

If you buy something and then sell it at a lower price, then you have a loss which is given by: Loss = buying price − selling price

The profit or loss can also be expressed as a percentage of buying price as follows:

Percentage Profit and Percentage Loss

Calculate percentage profit and percentage profit and percentage loss

Example 4

Mr. Richard bought a car for 3, 000, 000/− and sold for 3, 500, 000/−. What is the profit and percentage profit obtained?

Solution

Profit= selling price − buying price = 3,500,000-3,000,000=500,000

Therefore the profit obtained is 500,000/-

Example 5

Eradia bought a laptop for 780,000 tshs, and sell it for 720000 tshs, find the percentage loss.

Solution

But buying price = 780, 000/− and loss = buying price − selling price = 780, 000 − 720, 000 = 60, 000/−

**Simple Interest**

Simple Interest

Calculate simple interest

The amount of money charged when a person borrows money e. g from a bank is called interest (I)

The amount of money borrowed is called principle (P)

To calculate interest, we use interest rate (R) given as a percentage and is usually taken per year or per annum (p.a)

Example 6

Calculate the simple interest charged on the following

- 850, 000/− at 15% per annum for 9 months
- 200, 000/− at 8% per annum for 2 years

**Solution**

Real Life Problems Related to Simple Interest

Solve real life problems related to simple interest

Example 7

Mrs. Mihambo deposited money in CRDB bank for 3 years and 4 months. A t the end of this time she earned a simple interest of 87, 750/− at 4.5% per annum. How much had she deposited in the bank?

**Solution**

Given I = 87, 750/− R = 4.5% % T = 3 years and 4 months

Change months to years

Exercise 1

1. A metal is composed of copper and zinc in the ratio3:2 by volume. Find the volume of a piece of the metal which contains 42 cm

^{3 }of copper.
2. A person borrows tshs 40,000/= for a period of 6 years at 20% simple interest per annum. Calculate the total amount to be repaid.

3. A house was bought for tsh 1,500,000/= and sold for tsh 1,800,000/=. What was the percentage profit?

4. Tsh 2000/= was invested at 12% per annum simple interest. The investment is now worth tsh 2960/=. How many years ago was the money invested?

5. Abraham, Abdiel and Adon share 132000/=. Abraham gets 5/11 of the money, Abdiel gets 4/11 and Adon gets 2/11 of the money. How much does each get?

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