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A 6 litre solution is 45% alcohol. How many litres of pure alcohol mus

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Bunuel
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A 6 litre solution is 45% alcohol. How many litres of pure alcohol mus [#permalink] New post   29 Jan 2020, 03:07
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A 6 litre solution is 45% alcohol. How many litres of pure alcohol must be added to produce a solution that is 50% alcohol ?

A. 0.6
B. 1
C. 2.1
D. 3
E. 5.4
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A
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A 6 litre solution is 45% alcohol. How many litres of pure alcohol mus [#permalink] New post   29 Jan 2020, 03:52
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A 6 litre solution is 45% alcohol. How many litres of pure alcohol must be added to produce a solution that is 50% alcohol ?

Let's say that 45% alcohol and 55 % water in the solution:
(If pure alcohol is added, the amount of water in the solution is not changed.)

\((\frac{55}{100})*6= (\frac{11}{20})*6= \frac{33}{10}=3.3\) liters water --> 3.3 liters water should be 50 % of a new solution.

if 50% of a solution is water, whole solution should be 6.6 liters
--> 6.6 -6 = 0.6 liters pure alcohol must be added.

The answer is A.
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Re: A 6 litre solution is 45% alcohol. How many litres of pure alcohol mus [#permalink] New post   29 Jan 2020, 08:01
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ci*vi = cf*vf
6*.45 = vf*.5
vf= 5.4 ltrs
total addition to be done ; 6-5.4 ; 0.6
IMO A


Bunuel wrote:
A 6 litre solution is 45% alcohol. How many litres of pure alcohol must be added to produce a solution that is 50% alcohol ?

A. 0.6
B. 1
C. 2.1
D. 3
E. 5.4
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gracie
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Re: A 6 litre solution is 45% alcohol. How many litres of pure alcohol mus [#permalink] New post   29 Jan 2020, 13:01
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Bunuel wrote:
A 6 litre solution is 45% alcohol. How many litres of pure alcohol must be added to produce a solution that is 50% alcohol ?

A. 0.6
B. 1
C. 2.1
D. 3
E. 5.4


let a=liters of alcohol to be added
.45*6+a=.5(6+a)→
a=.6 liters
A
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Re: A 6 litre solution is 45% alcohol. How many litres of pure alcohol mus [#permalink] New post   29 Jan 2020, 13:41
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Bunuel wrote:
A 6 litre solution is 45% alcohol. How many litres of pure alcohol must be added to produce a solution that is 50% alcohol ?

A. 0.6
B. 1
C. 2.1
D. 3
E. 5.4


In 6 litres
Alcohol = 45% *6 = 2.7 litres
Water = 55%*6 = 3.3 litres

To make solution with 50% alcohol
Alcohol = 3.3 litres
Alcohol to be added = 3.3 - 2.7 = .6 litres

IMO A

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Re: A 6 litre solution is 45% alcohol. How many litres of pure alcohol mus [#permalink] New post   30 Jan 2020, 19:13
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I used alligation method

45% -------------100%
--------50------------
50----------------5
1------------------0.1
6-------------------0.6
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Re: A 6 litre solution is 45% alcohol. How many litres of pure alcohol mus [#permalink] New post   02 Feb 2020, 12:00
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Bunuel wrote:
A 6 litre solution is 45% alcohol. How many litres of pure alcohol must be added to produce a solution that is 50% alcohol ?

A. 0.6
B. 1
C. 2.1
D. 3
E. 5.4

Solution:

We can create the equation:

[(6 * 0.45) + n] / (6 + n) = 1/2

5.4 + 2n = 6 + n

n = 0.6

Alternate Solution:

To 6 liters of 45% alcohol we will add x liters of 100% alcohol, obtaining (6 + x) liters of 50% alcohol.

Let’s put this sentence into an equation:

6 (0.45) + x (1.00) = (6 + x) (0.50)

2.7 + x = 3 + 0.5x

0.5x = 0.3

x = 3/5 = 0.6

Answer: A
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Re: A 6 litre solution is 45% alcohol. How many litres of pure alcohol mus [#permalink] New post   13 Jun 2021, 13:46
Kinshook wrote:
Bunuel wrote:
A 6 litre solution is 45% alcohol. How many litres of pure alcohol must be added to produce a solution that is 50% alcohol ?

A. 0.6
B. 1
C. 2.1
D. 3
E. 5.4


In 6 litres
Alcohol = 45% *6 = 2.7 litres
Water = 55%*6 = 3.3 litres

To make solution with 50% alcohol
Alcohol = 3.3 litres
Alcohol to be added = 3.3 - 2.7 = .6 litres

IMO A

Posted from my mobile device





can you please explain how you took "Alcohol=3.3litre" under the To make solution with 50% alcohol part.
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Re: A 6 litre solution is 45% alcohol. How many litres of pure alcohol mus [#permalink] New post   15 Nov 2023, 07:58
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Re: A 6 litre solution is 45% alcohol. How many litres of pure alcohol mus [#permalink]
15 Nov 2023, 07:58
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