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    MATHEMATICS: FORM ONE: Topic 9 – RATIO, PROFIT AND LOSS

    Msomi BoraBy Updated:7 Mins Read

     

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    TOPIC 9: RATIO, PROFIT AND LOSS

    Ratio

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

    Examples of ratios

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

    NOTE: Ratios can be simplified like fractions

    1. 40: 45 = 8: 9
    2. 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

    1. Increase 6 in the ratio 4 ∶ 3
    2. 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

    1. 850, 000/− at 15% per annum for 9 months
    2. 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 cm3 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?

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

    Examples of ratios

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

    NOTE: Ratios can be simplified like fractions

    1. 40: 45 = 8: 9
    2. 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

    1. Increase 6 in the ratio 4 ∶ 3
    2. 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

    1. 850, 000/− at 15% per annum for 9 months
    2. 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 cm3 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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