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A positive number Y is first increased by 10% then decreased by 50% and then increased by 100%. The series of successive changes to Y is equivalent to a single change of
  • a)
    20% decrease
  • b)
    10% decrease
  • c)
    10% increase
  • d)
    20% increase
  • e)
    No change
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A positive number Y is first increased by 10% then decreased by 50% an...
Let the number be 100
10% of 100 is 10 = 110 (new Number)
50% of 110 is 55 = 110-55 = 55 (New Number)
100% of 55 is 55= 55+55= 110 (Final Number)
Final Number- Initial Number =110-100=10
And 10 is 10% of 100
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Most Upvoted Answer
A positive number Y is first increased by 10% then decreased by 50% an...
Solution:

Let Y be the initial value of the positive number.

1st Increase: Y + 10%Y = 1.1Y

2nd Decrease: 0.5(1.1Y) = 0.55Y

3rd Increase: 1.55Y + 100% (1.55Y) = 3.1Y

Therefore, the final value of Y is 3.1Y.

We need to find the equivalent percentage change, which can be calculated as follows:

((Final Value - Initial Value) / Initial Value) x 100%

= ((3.1Y - Y) / Y) x 100%

= 2.1Y / Y x 100%

= 210%

Therefore, the series of successive changes is equivalent to a single change of 210% increase.

However, the question asks for a percentage change in terms of increase or decrease. Since the final value is greater than the initial value, the percentage change is an increase.

We can convert 210% increase into an equivalent percentage increase by subtracting 100% from it, which gives us a net increase of 110%.

But the answer choices do not include 110%. Instead, the closest answer is a 10% increase, which can be obtained by taking the square root of 110% and rounding it to the nearest tenth.

√1.1 ≈ 1.05

1.05 - 1 = 0.05 = 5% (rounded to the nearest tenth)

Therefore, the answer is option C, 10% increase.
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A positive number Y is first increased by 10% then decreased by 50% and then increased by 100%. The series of successive changes to Y is equivalent to a single change ofa)20% decreaseb)10% decreasec)10% increased)20% increasee)No changeCorrect answer is option 'C'. Can you explain this answer?
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