Two different acid solutions were combined to create a 10-liter

Question

Two different acid solutions were combined to create a 10-liter mixture. The first solution contained 0.8 liters of acid, while the second solution contained 0.6 liters of acid. If the concentration of acid in the first solution was twice that of the second solution, what was the volume of the first solution?

A. 3.0 liters
B. 3.2 liters
C. 3.6 liters
D. 4.0 liters
E. 4.2 liters

Bunuel · Accepted Answer

Official Solution:

Two different acid solutions were combined to create a 10-liter mixture. The first solution contained 0.8 liters of acid, while the second solution contained 0.6 liters of acid. If the concentration of acid in the first solution was twice that of the second solution, what was the volume of the first solution?

A. 3.0 liters
B. 3.2 liters
C. 3.6 liters
D. 4.0 liters
E. 4.2 liters

Let  x  be the volume of the first solution. Since the total volume is 10 liters, the volume of the second solution is  10-x . Using the given information, we form the equation  \frac{0.8}{x} = 2*\frac{0.6}{10 - x} , representing the acid concentration in the first solution being twice that in the second solution. Solving for  x , we find the volume of the first solution to be  x = 4  liters.

Answer: D

ronneyc · Answer

4L


Let A be the volume of solution with 0.8L of acid
Let B be the volume of solution with 0.6L of acid

A+B=10L

since the percentage of acid in A equals twice perc of acid in B:
0.8/A = 2* (0.6/B)

Solving the 2 equations gives A=4L

LM · Answer

1st: X liter & Acid = 0.8L

2nd: Y liter & Acid = 0.6L

Given:

X+Y=10L.........( i )

(0.8/X)*100 = 2* 

Y=(1.5)*X

Therefore, ( i ) can be re-written as 

X+1.5X =10

X= 4Liter

fluke · Answer

Let the volume of the first solution in the mixture be "x" liters, the volume of the second solution in the mixture must be (10-x)

% of acid in 1st = (0.8/x)*100
% of acid in 2nd = (0.6/(10-x))*100

(0.8/x)*100 = 2*(0.6/(10-x))*100
8-0.8x = 1.2x
2x = 8
x=4 liters

Ans: "D"

KarishmaB · Answer

Responding to a pm:

First solution had .8 liters of acid and second had .6 liters. Total the 10 liters solution must have had .8 + .6 = 1.4 liters of acid in 10 liters of solution which is 14% (average %age)
If %age of acid in second solution is x, %age of acid in first solution is 2x. Say volume of first solution is w which means volume of second solution is (10 - w)

Let's see how x and w connect:
.8 = 2x% of w = 2xw/100
xw = 40

Weighted Average Formula:
Cavg = (C1*w1 + C2*w2)/(w1 + w2)
14 =  /10
140 =  
x = 10

Since xw = 40, w = 4

So volume of first solution is 4 liters.

PareshGmat · Answer

Solved using single variable:

Sol I ................. Sol II ............... Total

x ...................... 10-x ..................... 10
(Assume)

x has 0.8lts of acid; 10-x has 0.6lts of acid

Percentage of acid in the Sol I is twice that in Sol II

100 * \frac{0.8}{x} = 2 * 100 * \frac{0.6}{10-x}

x = 4

Answer = D

JeffTargetTestPrep · Answer

We can let x = the number of litres of the first solution (the one with 0.8 litres of acid), so 10 - x = the number of litres of the second solution (the one with 0.6 litres of acid). Since the percentage of acid in the first solution was twice that of the second solution, we can say:

0.8/x = 2 * 0.6/(10 - x)

0.8/x = 1.2/(10 - x)

1.2x = 8 - 0.8x

2x = 8

x = 4

Answer: D

Meena4 · Answer

Just one doubt. Actually the acid’s volume is given right, it’s the not technically the amount right. Amount is equal to volume and concentration. How can we assume the volume of the acid to be the amount, confused

Bunuel · Answer

In this problem, the volume of acid (0.8 liters and 0.6 liters) refers to the amount of pure acid present in solution 1 and solution 2. The concentrations describe how much of each solution is pure acid. So, when the question states that the first solution contains 0.8 liters of acid, it refers to the amount of pure acid, not the total volume of the solution.

Legallyblond · Answer

why cant we use alligation here?

SwethaReddyL · Answer

KarishmaB  - can you please do the scale method here?
so i tried like this,

0.6----------x---------0.8 since the weight is 1:2(as i have taken B first and A second) the difference ratio is 2:1
After this i am stuck, please help

KarishmaB · Answer

You have the average concentration (1.4/10). Weighted average will be used on individual concentrations which you do not have. You will need to take two variables to use weighted averages as shown here: https://gmatclub.com/forum/two-differen ... l#p1380936 Scale method is just the visual representation of the same formula. It is much better to do what Bunuel did above here: https://gmatclub.com/forum/two-differen ... l#p3467491

Two different acid solutions were combined to create a 10-liter

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