Question : When the price of an item was reduced by 20%, its sales increased by $x$%. If there is an increase of 25% in receipt of the revenue, then the value of $x$ is:
Option 1: 55.35
Option 2: 57.75
Option 3: 54.35
Option 4: 56.25
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Correct Answer: 56.25
Solution :
Effective change = $x+y+\frac{xy}{100}$
The increase takes the positive percentage values and the decreases take the negative percentage values of $x$ and $y$.
⇒ $x-20-\frac{20x}{100} = 25$
⇒ $x-\frac{x}{5} = 45$
⇒ $\frac{4x}{5} = 45$
⇒ $x = \frac{45×5}{4}= \frac{225}{4}=56.25$%
Hence, the correct answer is 56.25.
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