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Mixture problem

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Mixture problem

by Mo2men » Wed Jun 12, 2019 9:33 am
A vessel of capacity 2 liter has 25% of alcohol and another vessel of capacity 6 liter had 40% alcohol. Both liquids were poured out in one vessel.. What is approximately the new concentration of Mixture?

A) 20%
B) 30%
C) 37.5%
D) 50%
E) 66.67%

OA: C

Dear GMAT Guru

Can you please show the alligation method here?
Thanks
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by Ian Stewart » Wed Jun 12, 2019 1:37 pm
The answer needs to be between 25% and 40%, and because we're using more of the 40% solution, the answer must be closer to 40%, so only one answer makes sense, 37.5%. That's assuming both vessels are full, something the question needs to mention (but doesn't).

If you want to use alligation, you can draw a number line with the percentages for each component, and the overall percentage A in the middle:

---25-------d---------A---e--40----

Because the parts are in a 6 to 2, or 3 to 1 ratio, the distances I've labeled d and e are in a 3 to 1 ratio. So d is 3/4 of the total distance between 25 and 40, so is (3/4)(15) = 45/4 = 11.25, and A = 36.25.

I suppose that's "approximately" 37.5, but that's a very bizarre "correct" answer to this question when a number like 36 is a much better approximation. What is the source?
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by Scott@TargetTestPrep » Fri Jun 14, 2019 2:38 pm
Mo2men wrote:A vessel of capacity 2 liter has 25% of alcohol and another vessel of capacity 6 liter had 40% alcohol. Both liquids were poured out in one vessel.. What is approximately the new concentration of Mixture?

A) 20%
B) 30%
C) 37.5%
D) 50%
E) 66.67%

OA: C
(2 x 0.25 + 6 x 0.4)/(2 + 6) = (0.5 + 2.4)/8 = 2.9/8 ≈ 3/8 = 0.375 = 37.5%

Alternate Solution:

We start with 2 liters of 25% alcohol and add to it 6 liters of 40% solution, and the result is 8 liters of x% solution. Let's express this information as an equation:

2(0.25) + 6(0.40) = 8(x)

0.5 +2.4 = 8x

5 + 24 = 80x

29/80 = x

We can approximate this answer with 30/80 = ⅜ which is about 37.5%

Answer: C

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by GMATGuruNY » Sat Jun 15, 2019 2:02 am
Mo2men wrote:A vessel of capacity 2 liter has 25% of alcohol and another vessel of capacity 6 liter had 40% alcohol. Both liquids were poured out in one vessel.. What is approximately the new concentration of Mixture?

A) 20%
B) 30%
C) 37.5%
D) 50%
E) 66.67%

OA: C

Dear GMAT Guru

Can you please show the alligation method here?
Thanks
2 liters of 25% solution are combined with 6 liters of 40% solution.
Average percentage for the entire 8 liters = (2*25 + 6*40)/8 = 290/8 = 36.25.

The closest answer is C.

Alligation approach:

Let V1 and V2 = the two vessels and M = the mixture.

Step 1: Plot the three percents on a number line, with the percents for V1 and V2 on the ends and M in the middle.
V1 25-----------M-----------40 V2

Step 2: Calculate the distances between V1, M and V2.
This distances on the number of line are determined by the RECIPROCAL of the following ratio:
(volume of V1)/(volume of V2). = 2/6 = 1/3 = x/3x
Plotting the reciprocal of this ratio on the number line, we get:
V1 25----3x----M----x----40 V2

Step 3: Determine the value of x.
The number line indicates that the total distance (3x+x) is equal to the difference between 40 and 25:
3x+x = 40-25
4x = 15
x = 15/4 = 3.75

Since the percentage for M is x less than the percentage for V2, we get:
M = V2-x = 40-3.75 = 36.25

The closest answer is C.
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