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Excellent Method for Calculating Successive Percentages...

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Excellent Method for Calculating Successive Percentages...  [#permalink]

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New post 03 Oct 2014, 12:52
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For successive increase / decrease in percentages, for successive years / times, the following formula will come handy:

Let the successive increase in percentages be a% and b%.
In that case, the total increase will be (a + b + ab/100 )%

Lets try an example.

If the increase is 10% and 20 %, the successive increase will be (10 + 20 + 20 * 10/100) = 32 %.

If there's an increase and a decrease, in that case, the decrease will be considered a negative value.

Lets try an example.

If there's an increase of 20% and then a decrease of 10%, the successive percentage will be (20 + (-10) + 20 * (-10) / 100 ) = 20 - 10 - 2 = 8% increase.

Now in case of discounts, the value of discount percentages will be considered negative.

Lets try an example

If Kouton's give 50% + 50% off on independence day, what is the final discount given by Koutons

The discount percentage will be (-50 + (-50) + (-50) * (-50) / 100 ) = -100+25 = 75% discount.

This method is useful when the percentage increase / decrease if for lot many times.

Once this method is mastered, successive percentage calculation will be a cakewalk and would relieve you of the pain of picking up pencil and scribing on paper.. :-)

Hope the methods helps you all.
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Re: Excellent Method for Calculating Successive Percentages...  [#permalink]

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New post 12 Oct 2015, 06:40
thanks, very helpful
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Re: Excellent Method for Calculating Successive Percentages...  [#permalink]

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New post 18 Dec 2016, 07:49
2
UmangMathur wrote:
For successive increase / decrease in percentages, for successive years / times, the following formula will come handy:

Let the successive increase in percentages be a% and b%.
In that case, the total increase will be (a + b + ab/100 )%

Lets try an example.

If the increase is 10% and 20 %, the successive increase will be (10 + 20 + 20 * 10/100) = 32 %.

If there's an increase and a decrease, in that case, the decrease will be considered a negative value.

Lets try an example.

If there's an increase of 20% and then a decrease of 10%, the successive percentage will be (20 + (-10) + 20 * (-10) / 100 ) = 20 - 10 - 2 = 8% increase.

Now in case of discounts, the value of discount percentages will be considered negative.

Lets try an example

If Kouton's give 50% + 50% off on independence day, what is the final discount given by Koutons

The discount percentage will be (-50 + (-50) + (-50) * (-50) / 100 ) = -100+25 = 75% discount.

This method is useful when the percentage increase / decrease if for lot many times.

Once this method is mastered, successive percentage calculation will be a cakewalk and would relieve you of the pain of picking up pencil and scribing on paper.. :-)

Hope the methods helps you all.

how will it work for 4 or 5 such successive change?
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Re: Excellent Method for Calculating Successive Percentages...  [#permalink]

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New post 02 Oct 2017, 11:04
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what to do if three or more percentages are given?
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Re: Excellent Method for Calculating Successive Percentages...  [#permalink]

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New post 17 May 2018, 01:50
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shivanshig wrote:
what to do if three or more percentages are given?

anu311 wrote:
how will it work for 4 or 5 such successive change?

You should apply the formula between the 3rd percentage and the result obtained on the first pass (with the 1st and 2nd percentage).
You first calculate R1 = (a + b + ab/100), then you calculate R2 = (c + R1 + c R1/100).
Then between the 4th percentage and the result obtained on the two first passes (d + R2 + d R2/100), etc.

However, the formula is (a + b + c + abc/100) is not correct ! :roll:
The correct formula is (a + b + c + ab/100 + ac/100 + bc/100 + abc/10000) but it might be not useful to remember this... :-D
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Re: Excellent Method for Calculating Successive Percentages...  [#permalink]

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New post 22 May 2018, 22:28
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shivanshig wrote:
what to do if three or more percentages are given?



First of all, you will hardly get any question, with more than 3 successive percentage change.

    Even if you get 3, then you can use the given formula ( \(a + b + \frac{ab}{100}\)) twice to get the answer.

    However, if you really want a formula, then you can use this to get overall percentage when there is exactly three percentage change.

    Overall Percentage = \(a + b + c + \frac{(ab + bc + ca)}{100} +\frac{abc}{100^2}\)

Note these formula can be easily derived if you know how to find the final value of any number with successive change.

    Final Value = Initial Value (1 + a%) (1+b%)

    Final Value = Initial value ( 1 + a% + b% + a% * b%)

    Final Value/Initial Value = ( 1 + a% + b% + a% * b%)

    (Final Value - Initial Value)/Initial value = a% + b% + a*b%/100

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Excellent Method for Calculating Successive Percentages...  [#permalink]

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New post 24 May 2018, 03:30
EgmatQuantExpert wrote:
shivanshig wrote:
what to do if three or more percentages are given?



First of all, you will hardly get any question, with more than 3 successive percentage change.

    Even if you get 3, then you can use the given formula ( \(a + b + \frac{ab}{100}\)) twice to get the answer.

    However, if you really want a formula, then you can use this to get overall percentage when there is exactly three percentage change.

    Overall Percentage = \(a + b + c + \frac{(ab + bc + ca)}{100} +\frac{abc}{100^2}\)

Note these formula can be easily derived if you know how to find the final value of any number with successive change.

    Final Value = Initial Value (1 + a%) (1+b%)

    Final Value = Initial value ( 1 + a% + b% + a% * b%)

    Final Value/Initial Value = ( 1 + a% + b% + a% * b%)

    (Final Value - Initial Value)/Initial value = a% + b% + a*b%/100


EgmatQuantExpert could you please show how to use this formula (a+b+ab/100) twice for 3 successive percentages problem?
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Re: Excellent Method for Calculating Successive Percentages...  [#permalink]

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New post 24 May 2018, 03:56
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sadikabid27 wrote:

EgmatQuantExpert could you please show how to use this formula (a+b+ab/100) twice for 3 successive percentages problem?


Let me take an example to show the application.
    • Assuming that the value of a variable has been successively increased by 10%, 20%, and 40% respectively.
We need to calculate the overall percentage increase of value of that variable.

    • We take two percentages at a time, say 10% and 20%, and calculate the overall percentage increase as \(10 + 20 + \frac{10*20}{100}\) = 30 + 2 = 32%
    • Taking 32% and 40%, we can calculate the final value = \(32 + 40 + \frac{32*40}{100}\) = 72 + 12.8 = 84.8%

Hence, the overall percentage increase is 84.8%

Note that, we can consider the percentages in different order also, the end result will remain same.
    • Initially we are considering 10% and 40%.
    Percentage increase = \(10 + 40 + \frac{10*40}{100}\) = 50 + 4 = 54%
    • Next, we consider 54% and 20% to get the final result.
    Final percentage increase = \(54 + 20 + \frac{54*20}{100}\) = 74 + 10.8 = 84.8%
Hence, the overall percentage increase is 84.8%

If there is any decrease in percentage, the formula remains same. One only needs to consider the value as negative. (like if there is a 20% decrease, one needs to put -20 to calculate the change).
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Re: Excellent Method for Calculating Successive Percentages... &nbs [#permalink] 24 May 2018, 03:56
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