A Can Contains a Mixture of Two Liquids A and B in the Ratio 7:5 GMAT Problem Solving

Question: A can contains a mixture of two liquids A and B in the ratio 7:5 when 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially?

1. 45 litres
2. 36 litres
3. 28 litres
4. 25 litres
5. 21 litres

‘A can contains a mixture of two liquids A and B in the ratio 7:5’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills.
In GMAT Problem Solving section, examiners measure how well the candidates make analytical and logical approaches to solve numerical problems. In this section, candidates have to evaluate and interpret data from a given graphical representation. In this section, mostly one finds out mathematical questions. Five answer choices are given for each GMAT Problem solving question. 

Solution and Explanation:

Approach Solution 1:

Let us suppose that the can initially contain 7x and 5x litres of mixtures A and B respectively. The quantity of A in the mixture left
= [7x – (7/12)×9] litres
= [7x – 21/4] litres.
The quantity of B in mixture left
= [5x – (5/12)×9] litres
= [5x – 15/4] litres.
Therefore we can write: the ratio of the two quantities as
[7x – 21/4]/ [5x – 15/4] = 7/9
In other words, if we simplify the above equation, we get
252x – 189 = 140x + 147
252x-140x= 147+189
112x = 336
x=3
Therefore the can had 7(3) = 21 litres of the quantity A.
Thus the correct option is C.

Correct Answer: E

Approach Solution 2:
let A = 7x & B = 5x
total mixture = 7x+5x=12x
after 9 litre of mixture are drawn off remaining misture = 12x-9
after filling can with B:
A = (12x-9) * 7/12= 28x-21
B = {(12x-9)* 5/12}+9= 20x+21
So, (28x-21)/(20x+21)= 7/9
by solving above equation, we get
x=3
So liquid A was contained by the can initially = 7x = 7*3 = 21
Hence, C is the correct answer.

Correct Answer: E

Approach Solution 3:

Assume the can contains 7x and 5x litres of mixes A and B, respectively. The amount of A remaining in the combination is [7x - (7/12)9] litres = [7x - 21/4] litres.

The amount of B remaining in the combination is [5x - (5/12)9] litres = [5x - 15/4] litres.

As a result, the ratio of the two amounts is [7x - 21/4]/ [5x - 15/4] = 7/9.

To put it another way, 252x - 189 = 140x + 147

As a result, x = 3. As a result, the can contained 7(3) = 21 litres of amount A. As a result, C is the right answer.

Correct Answer: E

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