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A vessel has 30l of wine and 10l of water mixture . 4l of mixture is taken out from vessel and 4l of water is added.This process is repeated one more time.the ratio of quantity of wine is left and initial quantity of wine is :

I have tried:

Total quantity of vessel is:

40l

that is:

3:1

first time :4l of mixture is taken out

3x-3/4*4 : x-1/4*4 + 4 ( this four is water is added)

so

ratio becomes:

3x-3:x-3

second time process is continued :

(3x-3) -(3x-3)*4/4x-6 :(x-1) -(x-1)*4/4x-6 + 4 (four water is added)

for second time process i have framed the equation:

(3x-3) -(3x-3)*4/4x-6 + (x-1) -(x-1)*4/4x-6 + 4 = 4x - 2

x^2 is coming so please anyone guide me for what i am doing the mistake in framing the equation and solve it please

2 Answers 2

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Alternative Method -

Ratio = $\left( 1 - \frac{a}{x + y} \right)^n$

a is amount of water added.

x is quantity of wine.

y is quantity of water.

You can simply say x + y total solution.

n is number of time process repeated.

= $\left( 1 - \frac{4}{30 + 10} \right)^2$

= $\left( 1 - \frac{4}{40} \right)^2$

On solving you get 81:100

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    @Kanwalijit singh this equation equals 4x-2 correct ah? – 2017-01-30
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    ok try@Kanwalijit singh – 2017-01-30
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    Is any other method ok? – 2017-01-30
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    what i am doing mistake – 2017-01-30
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    ok tell another method @Kanwalijit singh , I will learn from you – 2017-01-30
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    How that formula derived@Kanwalijit singh – 2017-01-30
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    This is the shortcut formula for these type of questions. And I think no derivation for this available. – 2017-01-30
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    ok what type of questions we have to use this formula@Kanwalijit singh – 2017-01-30
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    ok Thankyou @Kanwalijit singh – 2017-01-30
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    If you have time and able to solve using my method , solve and show me the answer @Kanwalijit singh Thank you for spending time for this question – 2017-01-30
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    Yes I will definitely try your method. – 2017-01-30
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    Thankyou @Kanwalijit singh,after trying post it here itself – 2017-01-30
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    I am tried your method. And I got the main problem. In first case we know solution in 3:1 so we subtract 3 L from wine and 1 L from water. But after first case we have ratio 3x - 3 : x + 1. So we cant determine what part of 4 L subtracted from wine and what part from water. So its become more complex. – 2017-01-30
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    my method will not work ah?, they are blocking me from asking questions , please guide me for that – 2017-01-30
1

After the first exercise, wine left $30-\dfrac{30}{40}\cdot4=27$ unit

After the second exercise, wine left $27-\dfrac{27}{40}\cdot4=?$ unit

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    what i am doing Mistake ? @Lab bhattarchjee – 2017-01-30
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    (3x-3) -(3x-3)*4/4x-4 + (x-1) -(x-1)*4/4x-4 = 4x -4 this equation is correct ah? please anyone guide me from my point of view – 2017-01-30
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    please anyone guide me for the answer – 2017-01-30
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    I did not get any answer for this question till now – 2017-01-30
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    @elavarasan, Have u understood my method? Why are u introducing $x$ when the question is so plain & simple! – 2017-01-30
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    I did not understand your method,please explain @Lab bhattacharjee,I will learn from you – 2017-01-30
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    @elavarasan, Initially we had $30L$ wine. So, if we take out $4L$ mixture, the wine taken out will be $$\dfrac{30}{30+4}\cdot4=?$$ – 2017-01-30
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    ok , shall i call you as lab , ok then, ok I have understand then , for second time – 2017-01-30