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Excellent Method for Calculating Successive Percentages...

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Thoughtosphere
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Excellent Method for Calculating Successive Percentages... [#permalink] New post   Updated on: 20 Feb 2019, 04:12
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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 \((a + b + \frac{ab}{100})\%\)

Lets try an example:

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


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 \((20 + (-10) + \frac{20 * (-10)}{100}) = 20 - 10 - 2 = 8\%\) increase.

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 \((-50 + (-50) + \frac{(-50) * (-50)}{100}) = -100+25 = 75\%\) 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.

Originally posted by Thoughtosphere on 03 Oct 2014, 12:52.
Last edited by Bunuel on 20 Feb 2019, 04:12, edited 1 time in total.
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Re: Excellent Method for Calculating Successive Percentages... [#permalink] 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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Re: Excellent Method for Calculating Successive Percentages... [#permalink] New post   12 Oct 2015, 06:40
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thanks, very helpful
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Re: Excellent Method for Calculating Successive Percentages... [#permalink] New post   18 Dec 2016, 07:49
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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] 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] 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:
Show Spoiler
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] 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] 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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Excellent Method for Calculating Successive Percentages... [#permalink] New post   02 Apr 2020, 11:04
What my peers wrote is absolutely correct without any doubt.

You should know only one formulae, which is: A+B+[AxB]/[100]

Now as per the question you can put up the values.
Suppose if the question says;

1. There is an increase of A% and further there was an increase of B%, the formula would be: A + B + [A x B]/100.

2. There is an increase of A% and decrease of B%, the formula will be: A + (-B) + [A x (-B)]/100.
Note:- A "DISCOUNT" always denotes/implies to (-) sign.

3. If there was an discount of A% and furthermore discount of B% was given, the formula will be: -A + (-B) + [(-A) x (-B)]/100.

Remember the basic formulae and try to understand the what the test is trying to say, and you'll be able to answer it.
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Re: Excellent Method for Calculating Successive Percentages... [#permalink] New post   31 Mar 2023, 09:57
Final Value = Initial Value * (1 + Percent Increase/Decrease)^Number of Times Increased/Decreased

To use this formula, follow these steps:

Determine the initial value.
Determine the percentage increase or decrease.
Determine the number of times the value has increased or decreased.
Plug the values into the formula and solve for the final value.
For example, let's say the initial value is 100, the percentage increase is 10%, and the value has increased 3 times. Using the formula, we can calculate the final value as follows:

Final Value = 100 * (1 + 0.10)^3
Final Value = 100 * 1.331
Final Value = 133.1

Therefore, the final value after three successive increases of 10% is 133.1.

This method is useful because it allows you to quickly and easily calculate the final value after any number of successive percentage increases or decreases. It can be especially helpful in financial or business settings where you need to project future values based on past trends.
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Re: Excellent Method for Calculating Successive Percentages... [#permalink] New post   26 May 2023, 22:33
FOR EXAMPLE WE HAVA VALUE 120 AND THIS VALUE INCREASES BY 20 % THEN BY 25 % AND THEN BY 50 % , HOW TO APPLY THE FORMULA NOW?
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Re: Excellent Method for Calculating Successive Percentages... [#permalink]
26 May 2023, 22:33
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