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A number is increased first by 20% and then it is decreased by 30%. What is the percentage change in the number?
- a)16% decrease
- b)10% decrease
- c)20% decrease
- d)10% increase
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A number is increased first by 20% and then it is decreased by 30%. Wh...
Let the number be ‘x’.
Number after increasing it by 20% = x + (20% of x) = Rs. 1.20x
Number after decreasing it by 30% = 1.2x – (30% of 1.2x) = 0.7 × 1.2x = 0.84x
% change in the number = [(x – 0.84x)/x] × 100 = 16%
∴ The percentage change in the number = 16% decrease
Number after increasing it by 20% = x + (20% of x) = Rs. 1.20x
Number after decreasing it by 30% = 1.2x – (30% of 1.2x) = 0.7 × 1.2x = 0.84x
% change in the number = [(x – 0.84x)/x] × 100 = 16%
∴ The percentage change in the number = 16% decrease
Most Upvoted Answer
A number is increased first by 20% and then it is decreased by 30%. Wh...
Calculation of Percentage Change
To calculate the percentage change in the number after it is increased by 20% and then decreased by 30%, we can follow these steps:
Step 1: Increase the number by 20%
Let's assume the original number is 100.
After increasing it by 20%, the number becomes 100 + (100 * 20/100) = 120.
Step 2: Decrease the number by 30%
Now, we will decrease the number by 30%.
30% of 120 is (120 * 30/100) = 36.
Therefore, the new number after decreasing by 30% is 120 - 36 = 84.
Step 3: Calculate the percentage change
To calculate the percentage change, we use the formula:
Percentage Change = ((Final Value - Initial Value) / Initial Value) * 100
Plugging in the values, we get:
((84 - 100) / 100) * 100 = (-16 / 100) * 100 = -16%
Therefore, the percentage change in the number after it is increased by 20% and then decreased by 30% is a 16% decrease, which corresponds to option 'A'.
To calculate the percentage change in the number after it is increased by 20% and then decreased by 30%, we can follow these steps:
Step 1: Increase the number by 20%
Let's assume the original number is 100.
After increasing it by 20%, the number becomes 100 + (100 * 20/100) = 120.
Step 2: Decrease the number by 30%
Now, we will decrease the number by 30%.
30% of 120 is (120 * 30/100) = 36.
Therefore, the new number after decreasing by 30% is 120 - 36 = 84.
Step 3: Calculate the percentage change
To calculate the percentage change, we use the formula:
Percentage Change = ((Final Value - Initial Value) / Initial Value) * 100
Plugging in the values, we get:
((84 - 100) / 100) * 100 = (-16 / 100) * 100 = -16%
Therefore, the percentage change in the number after it is increased by 20% and then decreased by 30% is a 16% decrease, which corresponds to option 'A'.
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A number is increased first by 20% and then it is decreased by 30%. What is the percentage change in the number?a)16% decreaseb)10% decreasec)20% decreased)10% increaseCorrect answer is option 'A'. Can you explain this answer?
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