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A spirit and water solution is sold in a market. The cost pe

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A spirit and water solution is sold in a market. The cost pe [#permalink] New post 17 Mar 2014, 22:01
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A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 50 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?

A. 13
B. 33
C. 50
D. 51
E. 52
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Re: A spirit and water solution is sold in a market. The cost pe [#permalink] New post 17 Mar 2014, 22:36
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2 litres of 1/2 concentration spirit costs 50 cents = \frac{1}{2} dollars

2 litres of 1/3 concentration spirit will cost \frac{1}{3} dollars

3 litres of 1/3 concentration spirit will cost \frac{1}{3}*\frac{3}{2} dollars = \frac{1}{2} dollars = 50 cents

Answer is C
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Re: A spirit and water solution is sold in a market. The cost pe [#permalink] New post 17 Mar 2014, 23:17
MacFauz wrote:
2 litres of 1/2 concentration spirit costs 50 cents = \frac{1}{2} dollars

2 litres of 1/3 concentration spirit will cost \frac{1}{3} dollars

3 litres of 1/3 concentration spirit will cost \frac{1}{3}*\frac{3}{2} dollars = \frac{1}{2} dollars = 50 cents

Answer is C


Hi

how did you get 2 liters of 1/3 concentration of spirit will cost 1/3 dollars ?
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Re: A spirit and water solution is sold in a market. The cost pe [#permalink] New post 17 Mar 2014, 23:19
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The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has.

It means there is no effect of change in volume of water to the costing of the solution

So a solution of 1 liter of spirit and 2 liters of water will cost 50 cents

Answer = c = 50
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Re: A spirit and water solution is sold in a market. The cost pe [#permalink] New post 17 Mar 2014, 23:21
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It is given that the cost is directly proportional to the fraction of the spirit in volume.
50% spirit corresponds to 50 cents
So 33.33% spirit will correspond to 33.33 cents
qlx wrote:
MacFauz wrote:
2 litres of 1/2 concentration spirit costs 50 cents = \frac{1}{2} dollars

2 litres of 1/3 concentration spirit will cost \frac{1}{3} dollars

3 litres of 1/3 concentration spirit will cost \frac{1}{3}*\frac{3}{2} dollars = \frac{1}{2} dollars = 50 cents

Answer is C


Hi

how did you get 2 liters of 1/3 concentration of spirit will cost 1/3 dollars ?

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Re: A spirit and water solution is sold in a market. The cost pe [#permalink] New post 18 Mar 2014, 22:22
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qlx wrote:
The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has


This statment can also be re-stated as "The Cost of 1 litre of Spririt is 50 Cents and water is free".

If the mixture is changed by adding another litre of water, still the amount of Spirit in the solution is unchanged and you have pay only for the spirit.

Hence the price is also unchanged, 50 Cents.
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Re: A spirit and water solution is sold in a market. The cost pe [#permalink] New post 02 Apr 2014, 12:06
qlx wrote:
A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 50 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?

A. 13
B. 33
C. 50
D. 51
E. 52


I solved it as :

Cost = k (Part of spirit)

50cents = k (1/2) -------(1)
k=100

Now part (fraction of spirit in 3 Liters) 1/3

Cost=100(1/3) = 33.33 ----- (B)

I am not sure what is wrong with my understanding... :roll: :roll: :roll:

1L spirit + 1L water = 50% concentration
1L spirit + 2L water = 33.33% concentration

Logically price should be less for diluted liquid as in 1L solution spirit has reduced in parts per liter.
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Re: A spirit and water solution is sold in a market. The cost pe [#permalink] New post 03 Apr 2014, 01:34
Expert's post
PiyushK wrote:
qlx wrote:
A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 50 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?

A. 13
B. 33
C. 50
D. 51
E. 52


I solved it as :

Cost = k (Part of spirit)

50cents = k (1/2) -------(1)
k=100

Now part (fraction of spirit in 3 Liters) 1/3

Cost=100(1/3) = 33.33 ----- (B)

I am not sure what is wrong with my understanding... :roll: :roll: :roll:

1L spirit + 1L water = 50% concentration
1L spirit + 2L water = 33.33% concentration

Logically price should be less for diluted liquid as in 1L solution spirit has reduced in parts per liter.


You missed the following part: The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has.

According to the above the cost of each liter of the solution = k*\frac{s}{s+w}. So, s+w liters of the solution should cost k*\frac{s}{s+w}*(s+w)=ks. So, we can see that the price of the solution is based only the amount of the spirit there (s), which means that both solutions must have the same price because both have 1 liter of spirit.

Answer: C.
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Re: A spirit and water solution is sold in a market. The cost pe [#permalink] New post 03 Apr 2014, 03:09
Thanks Bunuel, I got it now.. I think I was sleeping while reading this question :P
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Re: A spirit and water solution is sold in a market. The cost pe [#permalink] New post 19 Apr 2014, 02:30
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Another Approach, a more mathematical one:

Cost/Ltr @ Concentration

Consider a constant of proportionality as K.

So,

Cost/Ltr = K * Conc.

Scenario 1:

50/2 = K * 1/2 => K=50

Scenario 2:

C/3 = K * 1/3

=> C=K

=>C=50
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Re: A spirit and water solution is sold in a market. The cost pe   [#permalink] 19 Apr 2014, 02:30
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