A music festival sells tickets online in advance of the event. This year, the organisers raised the price of a standard ticket by 8%, taking it to \(£54\). ...
Question 1 Report
A music festival sells tickets online in advance of the event. This year, the organisers raised the price of a standard ticket by 8%, taking it to \(£54\). Work out the price of a standard ticket before this increase was applied. (2)
Answer Details
Reversing a percentage increase means dividing by \((1+\text{the decimal rate})\), not multiplying, since the final price already represents the original price scaled up by that factor.
An 8% increase means the final price is \(108\%\), or \(1.08\) times, the original price. So the original price is found by dividing the final price by \(1.08\): \( £54 \div 1.08 = £50 \) [2 marks].
The trap in reverse-percentage questions is multiplying by \(1.08\) again (or by \(0.92\)) instead of dividing by \(1.08\); as a check, increasing £50 by 8% gives \( 50\times1.08=£54 \), which matches the final price given, confirming £50 is correct.
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