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

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

Answer = B = 1/2

Using allegation method:

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

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

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

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

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?

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

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

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

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.

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

\(\frac{40-0.15x}{100} = \frac{7}{20}\)

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

KarishmaB
Hi can you please explain the meaning of this part: What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
I solved it using allegation got 1:2, but inverted the answer to 2:1, since it is asked replaced : not replaced (assuming total quantity= 3, 2 parts of 40% solution is replaced and 1 part is remaining)