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# Excellent Method for Calculating Successive Percentages...

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Manager
Joined: 02 Jul 2012
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Location: India
Schools: IIMC (A)
GMAT 1: 720 Q50 V38
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Excellent Method for Calculating Successive Percentages...  [#permalink]

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Updated on: 20 Feb 2019, 03:12
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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, 11:52.
Last edited by Bunuel on 20 Feb 2019, 03:12, edited 1 time in total.
Formatted.
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Re: Excellent Method for Calculating Successive Percentages...  [#permalink]

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12 Oct 2015, 05:40
Intern
Joined: 01 Jan 2014
Posts: 16
Location: India
Concentration: Finance, Technology
GMAT 1: 500 Q34 V25
WE: Sales (Consulting)
Re: Excellent Method for Calculating Successive Percentages...  [#permalink]

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18 Dec 2016, 06:49
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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Joined: 01 Oct 2017
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Re: Excellent Method for Calculating Successive Percentages...  [#permalink]

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02 Oct 2017, 10:04
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what to do if three or more percentages are given?
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Joined: 17 May 2018
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Re: Excellent Method for Calculating Successive Percentages...  [#permalink]

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17 May 2018, 00:50
2
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 !
The correct formula is (a + b + c + ab/100 + ac/100 + bc/100 + abc/10000) but it might be not useful to remember this...
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Joined: 04 Jan 2015
Posts: 3410
Re: Excellent Method for Calculating Successive Percentages...  [#permalink]

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22 May 2018, 21:28
2
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]

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24 May 2018, 02:30
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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24 May 2018, 02:56
1

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]

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02 Apr 2020, 10:04
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.
Excellent Method for Calculating Successive Percentages...   [#permalink] 02 Apr 2020, 10:04