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Mixture problem

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Mixture problem

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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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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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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?

_________________
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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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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Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



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