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An item is discounted by 30% and then a further discount of 20% is applied to the reduced price - HSC - SSCE Mathematics Standard - Question 15 - 2023 - Paper 1

Question 15

An item is discounted by 30% and then a further discount of 20% is applied to the reduced price. What is the total percentage discount? A. 25% B. 44% C. 50% D. 56%

Worked Solution & Example Answer:An item is discounted by 30% and then a further discount of 20% is applied to the reduced price - HSC - SSCE Mathematics Standard - Question 15 - 2023 - Paper 1

Step 1

Calculate the first discount

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Answer

Let's assume the original price of the item is $P$ . The first discount of 30% reduces the price by:

$ext{First Discount} = 0.30 imes P = 0.3P$

The new price after the first discount is:

$P_{1} = P - 0.3P = 0.7P$

Step 2

Calculate the second discount applied to the reduced price

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Answer

The second discount of 20% is applied to the already reduced price ( $P_1$ ):

$ext{Second Discount} = 0.20 imes P_{1} = 0.20 imes 0.7P = 0.14P$

The new price after the second discount is:

$P_{2} = P_{1} - ext{Second Discount} = 0.7P - 0.14P = 0.56P$

Step 3

Calculate the total percentage discount

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Answer

The total amount discounted from the original price is:

$ext{Total Discount} = P - P_{2} = P - 0.56P = 0.44P$

To find the total percentage discount, we can use:

$ext{Total Percentage Discount} = rac{ ext{Total Discount}}{P} imes 100 = rac{0.44P}{P} imes 100 = 44\%$

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