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# A bartender removed from a bottle a certain quantity of a drink, which

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Math Expert
Joined: 02 Sep 2009
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A bartender removed from a bottle a certain quantity of a drink, which  [#permalink]

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23 Jul 2018, 23:30
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00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:42) correct 42% (01:43) wrong based on 110 sessions

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A bartender removed from a bottle a certain quantity of a drink, which had 25% alcohol content and replaced the same quantity with another drink that had an alcohol content of 10%. The alcohol content in the drink after replacement is 20%. What was the quantity of the drink that he replaced, if there was 1 litre of the drink in the bottle?

A. 1/5 litres
B. 1/4 litres
C. 1/3 litres
D. 1/2 litres
E. 2/3 litres

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Re: A bartender removed from a bottle a certain quantity of a drink, which  [#permalink]

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24 Jul 2018, 01:02

Solution

Given:
• A bartender removed from a bottle a certain quantity of a drink, which had 25% alcohol content and replaced the same quantity with another drink that had an alcohol content of 10%
• The alcohol content in the drink after replacement is 20%
• There was 1 litre of the drink in the bottle

To find:
• The quantity of the drink that was replaced

Approach and Working:
In the original solution,
• Water = 750 ml and Alcohol = 250 ml

Assume that the quantity that was replaced was 20n.
In that 20n,
• Water removed = 0.75 * 20n = 15n
• Alcohol removed = 0.25 * 20n = 5n

In the replaced 20n quantity,
• Water added = 0.9 * 20n = 18n
• Alcohol added = 0.1 * 20n = 2n

Hence, final value of
• Water = 750 – 15n + 18n = 750 + 3n
• Alcohol = 250 – 5n + 2n = 250 – 3n

As per the question,
• 250 – 3n = 20% of 1000 = 200
Or, 3n = 50
Or, n = $$\frac{50}{3}$$
Or, 20n = $$\frac{1000}{3}$$ ml = $$\frac{1}{3}$$ ltrs

Hence, the correct answer is option C.

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A bartender removed from a bottle a certain quantity of a drink, which  [#permalink]

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24 Jul 2018, 15:46
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Bunuel wrote:
A bartender removed from a bottle a certain quantity of a drink, which had 25% alcohol content and replaced the same quantity with another drink that had an alcohol content of 10%. The alcohol content in the drink after replacement is 20%. What was the quantity of the drink that he replaced, if there was 1 litre of the drink in the bottle?

A. 1/5 litres
B. 1/4 litres
C. 1/3 litres
D. 1/2 litres
E. 2/3 litres

The same unknown amount of liquid is removed and replaced
$$x$$ liters = unknown volume
$$.25=$$% alcohol of removed liquid
$$.10=$$% alcohol of replaced liquid
$$1L$$ = volume of liquid at beginning and end

We have 1 liter of 25% alchol liquid. $$x$$ liters are removed and replaced. Removed $$x$$ is 25% alcohol. Replaced $$x$$ is 10% alcohol. Result is 1 liter of 20% alcohol

Just as with other mixture problems, weighted average works

(1L*A%) - (removed*A%) + (replaced*B%) = (1L*C%)

$$(.25)(1L) - (.25)(x) +(.10)(x)=(.20)(1L)$$
$$.25L -.25x+.10x=.20L$$
$$.05L=.15x$$
$$x=\frac{.05}{.15}L=\frac{5}{15}L=\frac{1}{3}L$$

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Joined: 02 Aug 2009
Posts: 7107
Re: A bartender removed from a bottle a certain quantity of a drink, which  [#permalink]

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24 Jul 2018, 18:15
Bunuel wrote:
A bartender removed from a bottle a certain quantity of a drink, which had 25% alcohol content and replaced the same quantity with another drink that had an alcohol content of 10%. The alcohol content in the drink after replacement is 20%. What was the quantity of the drink that he replaced, if there was 1 litre of the drink in the bottle?

A. 1/5 litres
B. 1/4 litres
C. 1/3 litres
D. 1/2 litres
E. 2/3 litres

An apt case for weighted average method
So whatever is replaced is the quantity of 10% and initial solution still left is the quantity of 25%

So 25%...20%..............10%
Quantity of 10%=$$\frac{25-20}{25-10}=\frac{5}{15}=1/3$$
So 1/3 was replaced.

C
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Re: A bartender removed from a bottle a certain quantity of a drink, which  [#permalink]

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24 Jul 2018, 18:48
Bunuel wrote:
A bartender removed from a bottle a certain quantity of a drink, which had 25% alcohol content and replaced the same quantity with another drink that had an alcohol content of 10%. The alcohol content in the drink after replacement is 20%. What was the quantity of the drink that he replaced, if there was 1 litre of the drink in the bottle?

A. 1/5 litres
B. 1/4 litres
C. 1/3 litres
D. 1/2 litres
E. 2/3 litres

Let 'x' litres of quantity be withdrawn / re.

Now we know -
Alcohol withdrawn = 0.25x (25% of withdrawn quantity)
Hence Alcohol remaining in bottle = 0.25 (1-x) (25% of remaining quantity. 1 Litre is the total quantity in bottle(given) ) ----- (1)

We also know alcohol added is = 0.1x (10% of added quantity. Same quantity of total mixture is replaced) ----- (2)

New total alcohol content = 0.2 (1L) (20% of Total quantity in bottle i.e. 1 Litre) ------ (3)

Equation for alcohol content will be as follows -

Replaced alcohol + Remaining Alcohol = Total alcohol

i.e. (2) + (1) = (3)

=> 0.25(1-x) + 0.1x = 0.2(1L)
=> 0.25 - 0.25x + 0.1x = 0.2
=> 0.05 = 0.15x

Multiplying both sides by 100

=> 5 = 15x

therefore x = 1/3 Litres (which is the replaced quantity.)

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A bartender removed from a bottle a certain quantity of a drink, which  [#permalink]

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24 Jul 2018, 19:23
Bunuel wrote:
A bartender removed from a bottle a certain quantity of a drink, which had 25% alcohol content and replaced the same quantity with another drink that had an alcohol content of 10%. The alcohol content in the drink after replacement is 20%. What was the quantity of the drink that he replaced, if there was 1 litre of the drink in the bottle?

A. 1/5 litres
B. 1/4 litres
C. 1/3 litres
D. 1/2 litres
E. 2/3 litres

let x=litres of drink replaced
.25-.25x+.10x=.20
x=1/3 litres
C
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Re: A bartender removed from a bottle a certain quantity of a drink, which  [#permalink]

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25 Jul 2018, 16:48
Bunuel wrote:
A bartender removed from a bottle a certain quantity of a drink, which had 25% alcohol content and replaced the same quantity with another drink that had an alcohol content of 10%. The alcohol content in the drink after replacement is 20%. What was the quantity of the drink that he replaced, if there was 1 litre of the drink in the bottle?

A. 1/5 litres
B. 1/4 litres
C. 1/3 litres
D. 1/2 litres
E. 2/3 litres

Originally, we have 0.25 litres of alcohol in the 1-litre bottle of drink.

We can let x = the quantity being replaced. Thus 0.25x litres of alcohol is replaced by 0.1x litres of alcohol. Therefore, we have:

(0.25 - 0.25x + 0.1x)/(1 - x + x) = 0.2

0.25 - 0.15x = 0.2

0.05 = 0.15x

0.05/0.15 = x

1/3 = x

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Re: A bartender removed from a bottle a certain quantity of a drink, which  [#permalink]

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25 Nov 2018, 10:20
Bunuel wrote:
A bartender removed from a bottle a certain quantity of a drink, which had 25% alcohol content and replaced the same quantity with another drink that had an alcohol content of 10%. The alcohol content in the drink after replacement is 20%. What was the quantity of the drink that he replaced, if there was 1 litre of the drink in the bottle?

A. 1/5 litres
B. 1/4 litres
C. 1/3 litres
D. 1/2 litres
E. 2/3 litres

Weighted average method :
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Re: A bartender removed from a bottle a certain quantity of a drink, which &nbs [#permalink] 25 Nov 2018, 10:20
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