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Re: If there are 10 liters of a 20%-solution of alcohol, how much water sh [#permalink]
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aishumurali wrote:
How did u get 20 here ? 75% x 20 ?


Sorry 20 where ?

Could you be more precise sir ?
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If there are 10 liters of a 20%-solution of alcohol, how much water sh [#permalink]
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Since alcohol is not added and stays in the same amount, it's volume is 10*0.2=2 liters
\(\frac{2}{10+x}\)=\(\frac{1}{5}*\frac{1}{4}\), where 1/5 is 20% and 1/4 is 75% reduced amount
\(2*20=10+x\), \(x=30\). Answer is C
Carcass wrote:
If there are 10 liters of a 20%-solution of alcohol, how much water should be added to reduce the concentration of alcohol in the solution by 75% ?

A. 25 liters
B. 27 liters
C. 30 liters
D. 32 liters
E. 35 liters
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Re: If there are 10 liters of a 20%-solution of alcohol, how much water sh [#permalink]
Hi , Can this be termed as a right method too?

20% of alcohol in 10 li = 2 l
reducing this by 75 % makes the alochol content to be 0.5l
Now water content in the mixture is 9.5l which is 95 %
8 + X / 10 +x = 95/100
the answer of x litres of water be 30 .
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If there are 10 liters of a 20%-solution of alcohol, how much water sh [#permalink]
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You are reducing the actual alcohol content and we are asked that the concentration be reduced by \(75\)%

Consider this:

\(20\)% in \(10\) lit, so alcohol = \(2\)lit
Concentration is \(20\)% now, but when it is reduced by \(75\)%, then the new concentration will be \(\frac{1}{4}*20\)% \(= 5\)%

So now after the water is added the \(2\)lit alcohol will represent \(5\)% of the total mixture.
if \(5\)% = \(2\)lit, then \(100\)% will be \(40\)lit

So water added \(= 40 - 10 = 30\)lit

Answer C

aishumurali wrote:
Hi , Can this be termed as a right method too?

20% of alcohol in 10 li = 2 l
reducing this by 75 % makes the alochol content to be 0.5l
Now water content in the mixture is 9.5l which is 95 %
8 + X / 10 +x = 95/100
the answer of x litres of water be 30 .
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Re: If there are 10 liters of a 20%-solution of alcohol, how much water sh [#permalink]
I got the point , thank you so much :)
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Re: If there are 10 liters of a 20%-solution of alcohol, how much water sh [#permalink]
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After reducing alcohol you can apply short cut, every 0.5 l alcohol requires 9.5 l water. Hence, when alcohol is 2 l, water is 38 l. The difference between old volume of water and the required volume is 30 l.

IMO, you have good intuition
aishumurali wrote:
Hi , Can this be termed as a right method too?

20% of alcohol in 10 li = 2 l
reducing this by 75 % makes the alochol content to be 0.5l
Now water content in the mixture is 9.5l which is 95 %
8 + X / 10 +x = 95/100
the answer of x litres of water be 30 .


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Re: If there are 10 liters of a 20%-solution of alcohol, how much water sh [#permalink]
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