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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Question : If a number is increased by 25% and the resulting number is decreased by 25%, then the percentage increase or decrease finally is:
Option 1: no change
Option 2: decreased by $6\tfrac{1}{4}$%
Option 3: increased by $6\tfrac{1}{4}$%
Option 4: increased by $6$%
Question : A number is first increased by 16% and then increased by 20%. The number so obtained has now decreased by 40%. The net decrease percentage in the original number is:
Option 1: $16 \frac{12}{25}$%
Option 2: $15 \frac{9}{25}$%
Option 3: $11 \frac{13}{25}$%
Option 4: $13 \frac{7}{25}$%
Question : A number is first increased by 8% and then decreased by 3% to get 2619. What is 5% of that number?
Option 1: 125
Option 2: 135
Option 3: 130
Option 4: 140
Question : If the price of a product is first increased by 15% and then decreased by 20%, then what is the percentage change in the price?
Option 1: 5% decrease
Option 2: 8% increase
Option 3: 5% increase
Option 4: 8% decrease
Question : In a two-digit number, the digit at the unit place is 1 less than twice the digit at the tens place. If the digits at the units place and tens places are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is:
Option 1: $59$
Option 2: $23$
Option 3: $35$
Option 4: $47$
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