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

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

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

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

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.

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

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

Thanks Bunuel, I got it now.. I think I was sleeping while reading this question

Hi

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

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...

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.

'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

let x=cost of 3 liters of 1:2 solution
50/(2*1/2)=x/(3*1/3)
x=50¢

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

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

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.

1 out of 2 liter 50% of 2 liter is 2*50/100=1*1/2=1 1 liter cost 50cents
1 out of 3 liter 33.33% of 3 liter is 3*33/100 = 3*1/3=1 1 liter cost 50 cents



ans :C

Here's what the question is saying - the cost of solution increases with increase in volume of the spirit. Water is absolutely free of cost and has no effect on the overall cost of the solution. So basically, even if there was a mixture of 1 litre of spirit and 43 million litres of water, the cost of the solution would still be 50 cents (though that buyer would not really get high).

So curveball question?

Guys can you confirm my understanding? This is really all about knowing the relation.

c = ks
0.50 = k x (1 litre)
k = 0.50

Next,

c = ks
c = 0.50 x (1 litre)

The following would be incorrect

c = ks
0.50 = k x (1/2)
k = 1

c = 1 x (1/3) = 0.33