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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]

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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

Source: Nova GMAT
Difficulty Level: 750

Originally posted by qlx on 17 Mar 2014, 23:01.
Last edited by SajjadAhmad on 24 Jul 2019, 05:17, edited 1 time in total.
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Re: A spirit and water solution is sold in a market. The cost pe  [#permalink]

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New post 03 Apr 2014, 02:34
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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]

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New post 19 Apr 2014, 03:30
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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]

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New post 17 Mar 2014, 23:36
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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]

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New post 18 Mar 2014, 00:17
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]

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New post 18 Mar 2014, 00:19
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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]

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New post 18 Mar 2014, 00:21
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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]

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New post 18 Mar 2014, 23:22
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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]

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New post 02 Apr 2014, 13:06
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]

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New post 03 Apr 2014, 04:09
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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]

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New post 26 Jan 2015, 21:26
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



'Tis a tricky question. I had to reread it twice to notice it said "cost per liter of the solution is directly proportional to the part of spirit." That means the cost is still the same since there is 1 liter in both instances.

C. 50 cents
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Re: A spirit and water solution is sold in a market. The cost pe  [#permalink]

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New post 26 Jan 2015, 21:57
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peachfuzz 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



'Tis a tricky question. I had to reread it twice to notice it said "cost per liter of the solution is directly proportional to the part of spirit." That means the cost is still the same since there is 1 liter in both instances.

C. 50 cents


Yes, ensure that you understand the relation thoroughly!

Cost per liter = K * Fraction of Spirit

50 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 25 cents. Fraction of spirit is 1/2.

25 = K * (1/2)
K = 50

Cost per liter = 50 * (1/3) (1 part spirit, 2 parts water)
Cost for 3 liters = 50 * (1/3) * 3 = 50 cents
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Re: A spirit and water solution is sold in a market. The cost pe  [#permalink]

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New post 01 Jul 2016, 15:28
let x=cost of 3 liters of 1:2 solution
50/(2*1/2)=x/(3*1/3)
x=50¢
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Re: A spirit and water solution is sold in a market. The cost pe  [#permalink]

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New post 12 Jul 2017, 16:24
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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


When a solution has 1 liter of spirit and 1 liter of water, the solution has 2 liters of liquid with a spirit concentration of 1/2. Since the cost is 50 cents for 2 liters, the cost per liter is 25 cents. Now we can create an equation to find the proportional constant k:

(1/2) x k = 25

k = 50

Now we need to determine the cost of a solution that has 1 liter of spirit and 2 liters of water. We see that the solution has 3 liters of liquid with a spirit concentration of 1/3. Let’s first find the cost per liter, c:

(1/3) x k = c

(1/3) x 50 = c

50/3 = c

Since the cost per liter is 50/3 cents and there are 3 liters of solution, the cost of the solution is:

50/3 x 3 = 50 cents

Answer: C
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Re: A spirit and water solution is sold in a market. The cost pe  [#permalink]

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New post 18 Jul 2017, 23:07
2 L 50% sol costs=50 cents
1 L 50% sol costs=25 cents
1 L 33.33% sol costs=[25 x 33.33][/50] cents
3 L 33.33% sol costs=[25 x 33.33 x 3][/50] cents

3 L 33.33% sol costs=[25 x 100 x 3][/50 x 3] cents = 50 cents
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Re: A spirit and water solution is sold in a market. The cost pe  [#permalink]

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New post 16 Aug 2017, 00:22
Spirit and solution are sold in the market
Solution cost=amount of spirit in the solution ie anything else mixed has no effect on the price of the solution
First solution has 1 part spirit and 1 part water and price is=50 cents
As stated in 2nd line above the 50cent is the price of spirit.
1 part spirit and 2 part water will have price equal to the price of 1 part spirit which is 50 cents
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Re: A spirit and water solution is sold in a market. The cost pe  [#permalink]

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New post 18 Jan 2018, 11:06
2 lts soln. of 1/2 conc. costs 50 cents
1 lts soln. of 1/2 conc. costs 50/2 cents
1 lts soln. of 1 conc. costs (50/2)*2 cents
1 lts soln. of 1/3 conc. costs (50/2)*2*(1/3) cents
3 lts soln. of 1/3 conc. costs (50/2)*2*(1/3)*3 cents = 50 cents.

Ans. C

P.S. Wrote more steps for clarity. Hope it helps.
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