A certain quantity of 40% concentration solution is replaced with 25%

Question

A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?

A) 1:3
B) 1:2
C) 2:3
D) 2:1
E) 3:1

let x=amount of solution replaced
.4-.4x+.25x=.35
x=1/3
1-x=2/3=amount of solution not repaced
1/3:2/3=1:2
B

(A) 1:3
(B) 1:2
(C) 2:3
(D) 2:1
(E) 3:1

KarishmaB · Accepted Answer

This replacement question is nothing but a mixture problem with an extra step. Essentially, a certain amount of 40% solution is mixed with 25% solution to get 35% solution. The ratio of the amounts added will be given by:

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (25 - 35)/(35 - 40) = 2/1

So 40% solution amount:25% solution amount = 2:1 i.e. of total 3 parts of solution, 2 parts is 40% solution and 1 part is 25% solution.
So 1 part of the 40% solution was replaced and 2 parts of the 40% solution were not replaced.

Answer 1:2

EMPOWERgmatRichC · Answer

Hi notrandom,

Mixture questions can often be solved by using the Weighted Average Formula. Here's how you can set that up:

From the wording in the prompt, we're essentially mixing two liquids:

Liquid X is 40% concentrate
Liquid Y is 25% concentrate

We're supposed to mix some of each and end up with a solution that is 35% concentrate. The prompt doesn't give us specific amounts of liquids to work with and the question itself asks for the ratio of the two liquids, so we could even TEST VALUES if doing it that way made it easier for you. For now though, here's the Algebra:

X = # of ounces of liquid X
Y = # of ounces of liquid Y

(.4X + .25Y) / (X + Y) = .35

.4X + .25Y = .35X + .35Y
.05X = .1Y
5X = 10Y

From here, you have to be CAREFUL to answer the question that is ASKED.

5X = 10Y

Y/X = 5/10 = 1/2

For every 1 ounce of liquid Y (the replacement liquid), we had 2 ounces of liquid X (the original liquid).

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

Carcass · Answer

25% - - - - - - - - - 35% - - - - - - 40%

From 25 to 35 =10

From 35 to 40 = 5

So the ratio is 10/5 = 2 to 1

B it is

PareshGmat · Answer

Answer = B = 1/2

Using allegation method:

40 .................... 25

........... 35 ............

35-25 ..................... 40-35
=10 ...................... = 5

Answer = \frac{5}{10} = \frac{1}{2}

yosita18 · Answer

KarishmaB · Answer

We are given that a CERTAIN QUANTITY (we don't know how much) of a 40% solution (the concentration of spirit/sugar/... in the solution is 40%. So you have 40 ml spirit in 100 ml solution) is mixed with 25% concentration solution (the concentration of spirit/sugar/... in the solution is 25%). 
The final solution has concentration of 35% (the concentration of spirit/sugar/... in the solution is 35%). 
Now review the solution. Does it make sense?

gracie · Answer

A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?

A) 1:3
B) 1:2
C) 2:3
D) 2:1
E) 3:1

let x=amount of solution replaced
.4-.4x+.25x=.35
x=1/3
1-x=2/3=amount of solution not repaced
1/3:2/3=1:2
B

JeffTargetTestPrep · Answer

We let m = the amount of solution with 40% concentration and n = the amount of solution with 25% concentration.

Originally we have 0.4m concentration. Since the amount n is removed from m, 0.4n concentration is removed. Since the original amount n is replaced a new amount n, the total amount is still m, however, the 0.4n concentration that is removed is only replaced with 0.25n concentration. Thus we have:

(0.4m - 0.4n + 0.25n)/(m - n + n) = 0.35

(0.4m - 0.15n)/m = 0.35

0.4m - 0.15n = 0.35m

0.05m = 0.15n

5m = 15n

m = 3n

Since m = 3n and amount n is replaced, thus amount 2n is not replaced. Therefore, the ratio is 1/2.

Alternate Solution:

Let x = the original amount of 40% concentration and y = the amount that was taken out and replaced. Note that we started with x liters, and we ended with the same amount (because it was replaced).

Thus, we start with x liters of 40% solution, we take out y liters of 40% solution, and then add back y liters of 25% solution. The result is x liters of 35% solution. Converting the percents to decimals, we can create the equation:

0.40x – 0.40y + 0.25y = 0.35x

.05x = 0.15y

5x = 15y

x = 3y

The question is to determine the ratio of the solution that was replaced to the amount of solution that was not replaced. The amount of solution that was replaced is y, and the amount not replaced is (x – y). Thus, by substituting 3y for x, the ratio can be expressed as:

y/(x – y) = y/(3y – y) = y/2y = 1/2

Answer: B

AgarwalArpit20 · Answer

Let x be the quantity of 40% solution that was replaced by 25% solution.

The new concentration is now 35%

35% includes 'x' quantity of 25% solution and remaining quantity of 40% solution.

Remaining quantity = total quantity - x
where total quantity = 1 (since in fractions the total is 1)

Remaining quantity = 1-x

Equation: X*25% + (1-X)*40% = 35%
X = 5/15 = 1/3

Answer is B

praneethuddagiri · Answer

I will try solving this by using alligation:

40% 25%
 35%
10 5

So if you mix 40% and 25% in 10:5 or rather 2:1 ratio then you get 35% solution.
Now, replaced to not replaced is indeed 1:2.

dave13 · Answer

KarishmaB what s wrong with my solution

let initial quantity be 100 let x be number of liters removed \frac{(40-0.4x+0.25x)}{(60-0.6x+0.75x)} = \frac{40-015x}{60+0.15x} since final ratio is 35/100 i.e. 7/20 \frac{40-0.15x}{100} = \frac{7}{20}

KarishmaB · Answer

Nothing wrong. You get x = 33.33 litres (this much was removed and replaced)
So 66.66 litre was as it is i.e. 40% solution and 33.33 litre was 25% solution. 
So ratio of solution replaced : solution not replaced = 33.33 : 66.66 = 1:2

ravi1522 · Answer

Hello ,
This question i solved with weighted average
0.35=((100-x)*0.4+x*0.25)/100

so you get X as 33.33 and so rest will be 66.66 
so ratio will be 1:2 
Hence answer is B.

A certain quantity of 40% concentration solution is replaced with 25%

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