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Average, Ratio & Proportion, Percentage Quiz - ICSE Class 6 Mathematics

Free practice quiz: Average, Ratio & Proportion, Percentage (ICSE Class 6 Mathematics). 45 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

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Sample questions

  1. The ratio of two numbers is 3:5. If the sum of the numbers is 80, find the numbers.

    1. 25 and 55
    2. 30 and 50
    3. 24 and 56
    4. 35 and 45
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    Answer: B. 30 and 50

    Let the two numbers be 3x and 5x, as their ratio is 3:5. The sum of the numbers is given as 80. So, 3x + 5x = 80. This simplifies to 8x = 80. Dividing by 8, we get x = 10. The two numbers are therefore 3x = 3 * 10 = 30 and 5x = 5 * 10 = 50. We can check this: 30 + 50 = 80 and the ratio 30:50 simplifies to 3:5. Thus, the numbers are 30 and 50.

  2. If the ratio of the cost price to the selling price of an article is 5:6, then the percentage of profit is:

    1. 10%
    2. 15%
    3. 20%
    4. 25%
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    Answer: C. 20%

    Let the cost price (CP) be 5x and the selling price (SP) be 6x, as their ratio is 5:6. The profit is the difference between the selling price and the cost price: Profit = SP - CP = 6x - 5x = x. To calculate the percentage of profit, we use the formula: Percentage Profit = (Profit / CP) * 100. Percentage Profit = (x / 5x) * 100. Percentage Profit = (1/5) * 100 = 20%. Therefore, the percentage of profit is 20%.

  3. The ratio of apples to oranges in a basket is 5:3. If there are 32 fruits in total, how many apples are there?

    1. 15
    2. 18
    3. 20
    4. 24
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    Answer: C. 20

    Let the number of apples be 5x and the number of oranges be 3x, based on the ratio 5:3. The total number of fruits is the sum of apples and oranges: 5x + 3x = 32. This simplifies to 8x = 32. Dividing by 8, we get x = 4. The number of apples is 5x, so there are 5 * 4 = 20 apples. The number of oranges is 3x, so there are 3 * 4 = 12 oranges. Check: 20 apples + 12 oranges = 32 fruits. The ratio of apples to oranges is 20:12, which simplifies to 5:3. Thus, there are 20 apples.

  4. If 60% of a number is 90, what is 40% of that number?

    1. 50
    2. 55
    3. 60
    4. 65
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    Answer: C. 60

    Let the number be 'N'. We are given that 60% of N is 90. So, (60/100) * N = 90. This means 0.6 * N = 90. To find N, divide 90 by 0.6: N = 90 / 0.6 = 900 / 6 = 150. Now we need to find 40% of 150. 40% of 150 = (40/100) * 150 = 0.4 * 150 = 60. Therefore, 40% of the number is 60.

  5. If a number is decreased by 10% and then increased by 10%, what is the net percentage change?

    1. 1% decrease
    2. 1% increase
    3. 0% change
    4. 10% decrease
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    Answer: A. 1% decrease

    Let the original number be 100. When it is decreased by 10%, the new number becomes 100 - (10% of 100) = 100 - 10 = 90. When this new number (90) is increased by 10%, the increase amount is 10% of 90. 10% of 90 = (10/100) * 90 = 0.1 * 90 = 9. The new number after the increase is 90 + 9 = 99. The original number was 100, and the final number is 99. The net change is 99 - 100 = -1. This means there is a decrease of 1. As a percentage of the original number: (1 / 100) * 100 = 1%. So, there is a net 1% decrease. Using the shortcut formula: Net % Change = (x + y + xy/100)%. Here, x = -10% (decrease) and y = +10% (increase). Net % Change = (-10 + 10 + (-10 * 10) / 100)% = (0 + (-100) / 100)% = (0 - 1)% = -1%. A negative sign indicates a decrease.

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