The price of a commodity is reduced by 22.5%. By what percentage must the reduced price be increased so that the final price becomes 10% higher than the original price?
41.93%
Let the original price be \(P = 100\) for convenience.
After a reduction of 22.5%, the new price becomes \(100 - 22.5 = 77.5\).
The final price must be 10% higher than the original price, so it equals \(100 + 10 = 110\).
The increase required on the reduced price is \(110 - 77.5 = 32.5\).
The percentage increase on the reduced price is \(\frac{32.5}{77.5} \times 100 \approx 41.93\%\).
Hence, the reduced price must be increased by 41.93%.
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