A container has 40 gallons of solution that is 10% concentrate and 90%

Question

A container has 40 gallons of solution that is 10% concentrate and 90% water by volume. How many gallons of concentrate should be added to prepare a solution that is 20% concentrate and 80% water by volume?

(A) 5
(B) 10
(C) 40
(D) 80
(E) 240

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(A) 5
(B) 10
(C) 40
(D) 80
(E) 240

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Kinshook · Accepted Answer

Given: A container has 40 gallons of solution that is 10% concentrate and 90% water by volume. 
Asked: How many gallons of concentrate should be added to prepare a solution that is 20% concentrate and 80% water by volume?

Initial: -
Total = 40 gallons
Concentrate = 10%*40 = 4 gallons
Water = 90%*40 = 36 gallons

Let the gallons of concentrate added be x gallons

Concentrate = 4 + x gallons
Water = 36 gallons
Total = 40 + x gallons

(4+x)/(40+x) = 20%
4 + x = 8 + .2x
.8x = 4
x = 4/.8 = 5 gallons

IMO A

Ashu9876 · Answer

Sol. Initial Ratio of C and W = 1 : 9 = 4 : 36 
 Final ratio of C and W = 1 : 4 = 9 : 36 
Since amount of water is unchanged, change in ratio is due to the change in concentrate only which is 9 – 4 = 5 unit ratio, 
Initial ratio is 4 + 36 = 40 unit ratio which is equivalent to the 40 gallons. Hence value of 5 unit ratio will be equivalent to 5 gallons of concentrate. 
Hence Correct Answer is A.

Suvankar8250 · Answer

Concentrate can be considered as a solution with 100% concentration. Therefore, the equation of alligation and mixture comes out to be,
 (100-20)/(20-10) = 40/x , where x is the amount of concentrate
 
Solving the above equation, x comes out to be 5 gallons which is the answer.

ScottTargetTestPrep · Answer

The container has 40 x 0.1 = 4 gallons of concentrate and 40 - 4 = 36 gallons of water. We can let c = the number of gallons of concentrate needed to make it 20 percent concentrate and create the equation:

(4 + c)/(40 + c) = 1/5

20 + 5c = 40 + c

4c = 20

c = 5

Answer: A

joe123x · Answer

Straight forward test the questions.
X = 100% concentrate

The final solution will have 
4+X/40+X = 1/5

Subtitute the answers.
X = 5

9/ 45 = 1/5. Correct.

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ablatt4 · Answer

If the solution is 10% C and 90% W, that means we have 4gC and 36gW.

We are adding water to create a 20/80 solution.

If 36gW is constant then we just need to solve for what quantity is 36 80% of, which can be translated into 36/.8

36/(8/10) = 360/8=45

If we have 40g right now we need to add 5

A

lisahoang1301 · Answer

Let X be the gallons of concentration should be added:
    
 % concentrate 
 Volume (in gallons) 
 Volume of concentrate in the mixture 
 
  Original mixture 
 10% 
 40 
 40 * 10% = 4 gallons 
 
  Pure concentrate 
 100% 
 X 
 X * 100% = X 
 
  Mixture after adding concentrate 
 20% 
 40 + X 
 4 + X

We then have:
20% * (40+X) = 4 + X
Solve for X = 5 gallons

A container has 40 gallons of solution that is 10% concentrate and 90%

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	% concentrate	Volume (in gallons)	Volume of concentrate in the mixture
Original mixture	10%	40	40 * 10% = 4 gallons
Pure concentrate	100%	X	X * 100% = X
Mixture after adding concentrate	20%	40 + X	4 + X

GMAT Problem Solving (PS) Questions

A container has 40 gallons of solution that is 10% concentrate and 90%

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

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Perfect 805 Score Debrief by Julia

My Rewards