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A number is increased first by 20% and then it is decreased by 10%. What is the percentage change in the number?
- a)8% decrease
- b)10% decrease
- c)10% increase
- d)8% increase
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A number is increased first by 20% and then it is decreased by 10%. Wh...
Let the number be x
After increasing by 20%, x’ = x + 0.2x = 1.2x
After decreasing by 10%, x’’ = 1.2x - 0.1 × 1.2x = 1.08x
Clearly it is a % increase.
⇒ % increase = [(1.08x - x)/x] × 100 = 8% increase
Most Upvoted Answer
A number is increased first by 20% and then it is decreased by 10%. Wh...
Percentage Change in a Number
To find the percentage change in a number, we need to calculate the difference between the final value and the initial value, and then express it as a percentage of the initial value.
Given:
The number is first increased by 20% and then decreased by 10%.
Let's assume the initial value of the number is 'x'.
First Step: Increase by 20%
When we increase a number by a certain percentage, we multiply the number by 1 plus the percentage.
So, the number after increasing it by 20% will be:
x + (20/100)x
= x + 0.2x
= 1.2x
Second Step: Decrease by 10%
When we decrease a number by a certain percentage, we multiply the number by 1 minus the percentage.
So, the number after decreasing it by 10% will be:
1.2x - (10/100)(1.2x)
= 1.2x - 0.12x
= 1.08x
Final Step: Percentage Change
To find the percentage change, we calculate the difference between the final value and the initial value, and then express it as a percentage of the initial value.
Difference = Final Value - Initial Value
= 1.08x - x
= 0.08x
Percentage Change = (Difference / Initial Value) * 100
= (0.08x / x) * 100
= 0.08 * 100
= 8%
Therefore, the percentage change in the number is an 8% increase.
Correct answer: d) 8% increase
To find the percentage change in a number, we need to calculate the difference between the final value and the initial value, and then express it as a percentage of the initial value.
Given:
The number is first increased by 20% and then decreased by 10%.
Let's assume the initial value of the number is 'x'.
First Step: Increase by 20%
When we increase a number by a certain percentage, we multiply the number by 1 plus the percentage.
So, the number after increasing it by 20% will be:
x + (20/100)x
= x + 0.2x
= 1.2x
Second Step: Decrease by 10%
When we decrease a number by a certain percentage, we multiply the number by 1 minus the percentage.
So, the number after decreasing it by 10% will be:
1.2x - (10/100)(1.2x)
= 1.2x - 0.12x
= 1.08x
Final Step: Percentage Change
To find the percentage change, we calculate the difference between the final value and the initial value, and then express it as a percentage of the initial value.
Difference = Final Value - Initial Value
= 1.08x - x
= 0.08x
Percentage Change = (Difference / Initial Value) * 100
= (0.08x / x) * 100
= 0.08 * 100
= 8%
Therefore, the percentage change in the number is an 8% increase.
Correct answer: d) 8% increase
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A number is increased first by 20% and then it is decreased by 10%. What is the percentage change in the number?a)8% decreaseb)10% decreasec)10% increased)8% increaseCorrect answer is option 'D'. Can you explain this answer?
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