A bakery reduces the price of a birthday cake by 15% in a summer sale. The sale price is then reduced by a further 10% in a clearance sale. Show that the ov...
Question 1 Report
A bakery reduces the price of a birthday cake by 15% in a summer sale. The sale price is then reduced by a further 10% in a clearance sale.
- Show that the overall percentage reduction from the original price is 23.5%. (2)
- The original price of the cake was \(£40\). Work out the clearance sale price. (2)
Answer Details
This question tests combining two successive percentage reductions into a single overall percentage change, then applying it to a given original price.
A \(15\%\) reduction gives a multiplier of \(0.85\), and a further \(10\%\) reduction gives a multiplier of \(0.9\). Combined:
\[0.85 \times 0.9 = 0.765\]The overall reduction is \(1 - 0.765 = 0.235\), which is \(23.5\%\), as required [2 marks].
The clearance price is the original price multiplied by the combined multiplier:
\[£40 \times 0.765 = £30.60\][2 marks]
Adding the two percentages directly (\(15\% + 10\% = 25\%\)) would be incorrect, because the second reduction is taken off the already-reduced sale price, which is smaller than the original price.
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