Question : A number is first decreased by 20%. The decreased number is then increased by 20%. The resulting number is less than the original number by 20. Then the original number is:
Option 1: 200
Option 2: 400
Option 3: 500
Option 4: 600
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Correct Answer: 500
Solution :
Let $x$ be the initial value.
The number becomes 0.8$x$ after being reduced by 20%.
The number becomes 1.2 × (0.8$x$) = 0.96$x$ after increasing by 20%. This is 20 less than the initial number.
According to the question,
0.96$x$ = $x$ – 20
⇒ 0.04$x$ = 20
⇒ $x$ = 500
Hence, the correct answer is 500.
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