The percentage by which the price increased is; 16%
Let the price of an item be denoted as x
Now, we are told that the price of the item increased by 45%. Thus means that the price will be; 1.45x
Now, the price after inflation decreased by 20% or 0.2. Thus;
Final price is now; 1.45x(1 - 0.2)
⇒ 0.8(1.45x)
⇒ 1.16 x
Since the original price is x, then;
Difference in price = 1.16x - x
Difference in price = 0.16x
In percentage, this difference in price represents a 16% increase.
The complete question is;
Due to inflation, the price of an item increased by 45% and then dropped by 20%. By what percent did the price increase?
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