A can contains a mixture of two liquids A and B in proportion 3:5. Whe

Amount of A in solution = X*3/8
Amount of A taken out = 16*3/8
Resultant Amount of X in solution = X * 1/3

3X/8 - 16*3/8 = X/3
X=144

Calculate X*3/8 for the answer -> 144 * 3/8 = 54

I used the replacement theory described here
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/01 ... -mixtures/

Note that in the entire replacement process,
a) Mixture is homogenous (as its all liquid).Old Mixture:- \(\frac{A}{B}\) = \(\frac{3}{5}\). New mixture = \(\frac{A}{B}\) = \(\frac{1}{2}\)
Therefore old concentration \(A =\frac{ 3}{8}, B = \frac{5}{8}\).... Volume = \(8x\)
b) Quantity of A is untouched (constant) => \(\frac{3}{8}\) in 8x will be changed to \(\frac{1}{3}\) after \(16\)L of B is replaced by pure melted chocolate
c) quantity of B is varying (B is being added to change the concentration)

Hence going by the replacement formula,
we have to go by A (constant)

Ci*Vi = Cf*Vf
\(\frac{3}{8}(8x-16) = \frac{1}{3 }8x\)
x=\(\frac{144}{8}\) = \(18\)
AInitial Volume = \(18*3\) =\( 54\)L

Answer: D

There are many ways to do this. Let's discuss 2 such methods:

Method 1 (More logic based): After removal of the mixture, the ratio of A and B does NOT change. Thus, we still have A : B = 3 : 5
We now add B and the ratio changes to 1 : 2
However, we must keep the value for A unchanged since we did not change A while adding B.
Thus, we rewrite the new ratio of A : B as 3 : 6
Hence, we see that B has increased by 1. But, we know that this '1' actually represents 16L
Thus, A : B = 3 : 5 implies that A + B was '8', which actually equals 16 x 8 = 128L
This is AFTER 16L of the mix was removed.
Thus, the initial volume was 128 + 16 = 144L
Hence, volume of A = 3/(3+5) * 144 = 3 * 18 = 54L

Answer D


Method 2 (Alligation - anyone?): After removal of the mixture, the ratio of A and B does NOT change. Thus, we still have A : B = 3 : 5

Initial proportion of A = 3/8
Proportion of A added = 0
Final proportion of A = 1/3
Thus, we have:

Answer D

Let initial total = x lts
We need to find out 3x/8

After the substitution of 16 lts,
remaining A = 3(x-16)/8
remaining B = 5(x-16)/8 + 16
ratio of remaining A and remaining B = 1/2
Solving for x, x=144
So 3x/8 = 54

Answer is D

Harsha
GMAT Tutor | gmatanchor.com