Mixtures

[riz_gmat]

A solution contains 8 parts water for every 7 parts of lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 40% lemonade syrup?
(A)1.5
(B)1.75
(C)2.14
(D)2.34
(E)2.64

OA is C

[Uva@90]

A solution contains 8 parts water for every 7 parts of lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 40% lemonade syrup?
(A)1.5
(B)1.75
(C)2.14
(D)2.34
(E)2.64

OA is C

Hi Riz_Gmat,

Solution contains = 8 part of water:7 parts of lemonade, so total =15 parts

Our end solution should contain 40% Lemonade i.e 15*(40/100) =6 parts of lemonade

We need to reduce from 7 to 6 , 7-6 = 1 parts of lemonade should be removed.

15:7
x:1
so x = 15/7 => ~2.14

Hence Answer is C

Regards,
Uva.

[GMATGuruNY]

A solution contains 8 parts water for every 7 parts of lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 40% lemonade syrup?
(A)1.5
(B)1.75
(C)2.14
(D)2.34
(E)2.64

OA is C

Let W = the pure water, S = the original solution, and M = the mixture.

The following approach is called ALLIGATION -- a very good way to handle MIXTURE PROBLEMS.
Alligation can be performed only with fractions or percentages.

Step 1: Convert any ratios to FRACTIONS.
W:
Here, water/total = 1/1.
S:
Since water:lemonade = 8:7, and 8+7=15, water/total = 8/15.
M:
Since the mixture is to be 40% lemonade, water/total = 60/100 = 3/5.

Step 2: Put the fractions over a COMMON DENOMINATOR.
W = 1/1 = 15/15.
S = 8/15.
M = 3/5 = 9/15.

Step 3: Plot the 3 numerators on a number line, with the numerators of W and S on the ends and the numerator for M in the middle.
W 15----------------9------------------8 S

Step 4: Calculate the distances between the numerators.
W 15-------6--------9---------1--------8 S
-
Step 5: Determine the ratio in the mixture.
The ratio of W to S in the mixture is equal to the RECIPROCAL of the distances in red.
W:S = 1:6.

Since W:S = 1:6, for every 7 liters of mixture, 1 liter of pure water must be combined with 6 liters of original solution.
Thus, 1/7 of every 15 liters must come from the pure water:
(1/7) * 15 = 2.14.

The correct answer is C.

For two other problems that I solved with alligation, check here:

https://www.beatthegmat.com/ratios-fract ... tml#484583

[riz_gmat]

Hi GMATGuruNY,

Thankyou so much for the detailed explanation.

I got the answer till 1/7 parts. Still I dont get the last step,

Thus, 1/7 of every 15 liters must come from the pure water:
(1/7) * 15 = 2.14.

Here the question is

How many parts of the solution should be removed and replaced with water

, why cant we say 1/7 parts of solution must be removed and replaced with water?

[GMATGuruNY]

I got the answer till 1/7 parts. Still I dont get the last step,

The problem isn't well-worded.
It intends to ask the following:

A 15-liter tank contains a solution composed of 8 liters of water and 7 liters of lemonade syrup. How many liters of the solution should be removed and replaced with pure water so that lemonade syrup will constitute 40% of the resulting mixture?

(A)1.5
(B)1.75
(C)2.14
(D)2.34
(E)2.64

As shown in my solution above, the ratio of water to original solution in the resulting mixture = W:S = 1:6.
Implication:
In order for lemonade syrup to constitute 40% of the resulting mixture, for every 1 liter of pure water, there must be 6 liters of original solution.
Thus, in every 7 liters of the resulting mixture, water/total = 1/7.

Thus, 1/7 of the original 15 liters must be replaced with pure water:
(1/7) * 15 = 2.14.

[vipulgoyal]

alt approach
let x ammount of solution replaced with water
{7 - (7/15)x}/15 = 2/5
x= 75/35 = 2.14