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A worker received a 10% pay increase in 2017 and a further 10% pay increase in 2018 - OCR - GCSE Maths - Question 11 - 2021 - Paper 1

Question 11

A worker received a 10% pay increase in 2017 and a further 10% pay increase in 2018. The worker says Over these two years, my pay increased by 10% * 10% = 20%. The w... show full transcript

Worked Solution & Example Answer:A worker received a 10% pay increase in 2017 and a further 10% pay increase in 2018 - OCR - GCSE Maths - Question 11 - 2021 - Paper 1

Step 1

Calculate the pay after the first increase

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Answer

Let the original pay be represented as $P$ . After a 10% increase in 2017, the new pay becomes:

$P_1 = P + 0.10P = 1.10P$

Step 2

Calculate the pay after the second increase

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Answer

In 2018, the worker receives another 10% increase based on the new pay $P_1$ . Thus, the pay after the second increase is:

$P_2 = P_1 + 0.10P_1 = 1.10 imes 1.10P = 1.21P$

Step 3

Determine the total pay increase

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Answer

To find the total percentage increase, we compare the final pay $P_2$ with the original pay $P$ :

$ext{Increase} = P_2 - P = 1.21P - P = 0.21P$

The percentage increase is then calculated as:

$ext{Percentage Increase} = \left( \frac{0.21P}{P} \right) \times 100 = 21\%$

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