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Tom buys a radio for £40 - OCR - GCSE Maths - Question 9 - 2019 - Paper 1

Question 9

Tom buys a radio for £40. Later he sells it and makes a profit of 20%. Tom says The ratio of the price I paid for the radio to the price I sold the radio is 5 : 6.... show full transcript

Worked Solution & Example Answer:Tom buys a radio for £40 - OCR - GCSE Maths - Question 9 - 2019 - Paper 1

Step 1

Calculate the Selling Price

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Answer

To find the selling price of the radio, we first need to calculate 20% of the purchase price of £40.

First, we find the profit:

ext{Profit} = 20\% \times 40 = \frac{20}{100} \times 40 = 8.

Therefore, the selling price is:

\text{Selling Price} = \text{Purchase Price} + \text{Profit} = 40 + 8 = £48.

Step 2

Find the Ratio

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Answer

Now that we have both the purchase price and the selling price, we can find the ratio of the price paid to the price sold:

\text{Ratio} = \frac{\text{Purchase Price}}{\text{Selling Price}} = \frac{40}{48}.

To simplify this ratio, we can divide both the numerator and the denominator by 8:

\text{Ratio} = \frac{40 \div 8}{48 \div 8} = \frac{5}{6}.

Step 3

Conclusion

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Answer

Thus, the ratio of the price Tom paid for the radio to the price he sold it for is indeed 5 : 6, confirming that Tom is correct.

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