[discia] GCSE Maths › Ratio and Proportion › Repeated Percentage Change

Repeated Percentage Change

discia.org 10 questions · 32 marks
Name Date
  1. Calculator 1 mark
    Here is a sign in a shop.

    SALE
    10% OFF ALL ITEMS
    TODAY ONLY 10% OFF THE REDUCED PRICE
    THAT MEANS YOU SAVE 23%

    Is the sign correct? Tick a box. Yes / No Give a reason for your answer.
    Show answer
    No. 10% off then 10% off is a multiplier of \(0.9 \times 0.9 = 0.81\), so the true saving is 19%, and the sign says 23%.
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  2. Calculator 3 marks

    Callum buys a flat for £160,000.

    In the first year the value of the flat rises by 25%.

    In the second year the value of the flat falls by 5%.

    Find the value of the flat at the end of the second year.

    Show answer
    \(\text{£}190,000\)
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  3. Calculator 2 marks

    Ticket prices at a theme park increase by 8.2% each year.

    Show that after 14 years the ticket prices at the park will be at least treble their present level.

    Show answer
    The yearly multiplier is \(1.082\), so after 14 years the amounts are multiplied by \(1.082^{ 14 } \approx 3.014\). Since 3.014 is greater than 3, they will be at least treble their present level.
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  4. Calculator 3 marks

    A ferry company had 50,000 passengers last year.

    The number of passengers is predicted to increase by 8% this year and then to decrease by 7% next year.

    Is the predicted number of passengers for next year fewer than 50,300? You must show your working.

    Show answer
    Yes — this year \(50000 \times 1.08 = 54000\), and next year \(54000 \times 0.93 = 50220\), which is fewer than 50300.
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  5. Calculator 3 marks

    Erin owes an amount of £1000.

    Each month, Erin pays back 15% of the amount still owed.

    Erin says, "After three months I will still owe less than £630.00."

    Show working to check if her claim is correct.

    Show answer
    Yes — after 3 months £614.13 is still owed, which is less than £630.00, so the claim is correct.
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  6. Calculator 3 marks

    The number of members of a sports club is expected to increase by 6.1% each year.

    Assume there are now 900 members.

    Work out the expected number of members after 8 years.

    Give your answer to the nearest whole number.

    You must show your working.

    Show answer
    \(1445\)
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  7. Calculator 4 marks

    During 2018 the population of a village rose by 15%.

    During 2019 the population of the village fell by 40%.

    (a)

    Calculate the single number that the population of the village at the start of 2018 must be multiplied by to give the population of the village at the end of 2019.

    (b)

    Calculate the overall percentage change in the population of the village over the two years.

    Show answer
    (a) \(0.69\)
    (b) a 31% decrease
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  8. Calculator 5 marks

    A bike shop increases the price of everything it sells by 15%.

    Three months later it reduces every price by 15% in a sale.

    Before the increase, a helmet cost £104.

    (a)

    Work out the sale price of a helmet.

    (b)

    Anya says that the sale price is the same as the price before the increase.

    Explain why she is wrong.

    Show answer
    (a) \(\text{£}101.66\)
    (b) The 15% reduction is taken off £119.60, not off the original £104, so it takes off £17.94 when the increase only added £15.60. The sale price ends up 2.25% lower than the original price.
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  9. Calculator 5 marks

    Callum invests £4,900 in a savings bond.

    The value of the investment increases by 9% in the first year, by 6% in the second year and by 3% in the third year.

    (a)

    Calculate the value of the investment at the end of the third year.

    Give your answer correct to the nearest penny.

    (b)

    Calculate the overall percentage increase over the three years.

    Give your answer correct to 1 decimal place.

    Show answer
    (a) \(\text{£}5831.30\)
    (b) \(19.0\%\)
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  10. Calculator 3 marks

    Noah opens a savings account with £7,100.

    At the end of each year, the account pays 4.5% interest on the amount currently in it. As soon as the interest has been added, he pays in a further £1,900.

    He takes no money out of the account.

    Work out the amount in the account at the end of the second year.

    Give your answer to the nearest penny. Do not round any amount until you have your final answer.

    Show answer
    \(\text{£}11638.88\)
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discia.org Repeated Percentage Change · sheet 1
Answers Repeated Percentage Change · sheet 1
  1. No. 10% off then 10% off is a multiplier of \(0.9 \times 0.9 = 0.81\), so the true saving is 19%, and the sign says 23%.
  2. \(\text{£}190,000\)
  3. The yearly multiplier is \(1.082\), so after 14 years the amounts are multiplied by \(1.082^{ 14 } \approx 3.014\). Since 3.014 is greater than 3, they will be at least treble their present level.
  4. Yes — this year \(50000 \times 1.08 = 54000\), and next year \(54000 \times 0.93 = 50220\), which is fewer than 50300.
  5. Yes — after 3 months £614.13 is still owed, which is less than £630.00, so the claim is correct.
  6. \(1445\)
  7. (a) \(0.69\)
    (b) a 31% decrease
  8. (a) \(\text{£}101.66\)
    (b) The 15% reduction is taken off £119.60, not off the original £104, so it takes off £17.94 when the increase only added £15.60. The sale price ends up 2.25% lower than the original price.
  9. (a) \(\text{£}5831.30\)
    (b) \(19.0\%\)
  10. \(\text{£}11638.88\)
discia.org Repeated Percentage Change · sheet 1