Two Vessels Contain a Mixture of Spirit and Water GMAT Problem Solving

Question: Two vessels contain a mixture of Spirit and water. In the first vessel the ratio of Spirit to water is 8 : 3 and in the second vessel the ratio is 5 : 1. A 35 liter cask is filled from these vessels so as to contain a mixture of Spirit and water in the ratio of 4 : 1. How many liters are taken from the first vessels ?

(A) 11 liters
(B) 16.5 liter
(C) 22 liters
(D) 27.5 liters
(E) none of these

Correct Answer: A

Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given:

• Two vessels contain a mixture of Spirit and water.
• In the first vessel, the ratio of Spirit to water is 8 : 3
• In the second vessel, the ratio is 5 : 1.
• A 35-litre cask is filled from these vessels so as to contain a mixture of Spirit and water in a ratio of 4 : 1.

Find out:

• The litres taken from the first vessels.

Converting these ratios to the same total,

Now, the final ratios of the two solutions will be
1st vessel : 2nd vessel
(275 - 264) : (264 - 240)
=> 11 : 24

As the final solution is 35 litres, the first solution will be
11/(11+24)∗35
= 11 litre

Hence, the litres taken from the first vessels = 11 litres

Approach Solution 2:
The problem statement informs that:
Given:

• Two vessels contain a mixture of Spirit and water.
• In the first vessel, the ratio of Spirit to water is 8 : 3
• In the second vessel, the ratio is 5 : 1.
• A 35-litre cask is filled from these vessels so as to contain a mixture of Spirit and water in a ratio of 4 : 1.

Find out:

• The litres taken from the first vessels.

Let the solution in container A = 8x:3x (where 8x is spirit and 3x is water)
the solution in container B = 5y:1y (where 5y is spirit and 1y is water)
The new vessel has a capacity of 35 litres,
It contains a 4:1 ratio of spirit and water.
That means 28 litre spirit and 7 litre water.

Therefore,
8x+5y = 28 ----------(1)
3x+y = 07 ----------(2)
Multiply the second equation with 5
Therefore,
8x+5y = 28
15x+5y = 35
Equating both
x = 1

So the quantity taken first vessel
= 8x+3x
= 8+3
= 11

Hence, the litres taken from the first vessels = 11 litres

Approach Solution 3:
The problem statement suggests that:
Given:

• Two vessels contain a mixture of Spirit and water.
• In the first vessel, the ratio of Spirit to water is 8 : 3
• In the second vessel, the ratio is 5 : 1.
• A 35-litre cask is filled from these vessels so as to contain a mixture of Spirit and water in a ratio of 4 : 1.

Find out:

• The litres taken from the first vessels.

As per the question, we know that:
Sprit : Water
8 : 3 (first vessel)
5 : 1 (second vessel)

In 35L of the cask, 28L is spirit and 7L is water.

Let the first vessel has X Liter
the second vessel has Y Liter

Therefore, According to the question,
(8X+5Y)/(3X+1Y)=28/7
=>X/Y=1/4

Hence, the Final Ratio => Sprit : Ratio
8*1 : 3*1
and 5*4 : 1*4

Therefore,(8+3)=11L of the first vessel and (20+4)=24L of the second vessel will make 35 L.

Hence, the litres taken from the first vessels = 11 litres.

“Two vessels contain a mixture of Spirit and water”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. The candidate must have basic knowledge of mathematics and calculations to solve GMAT Problem Solving questions. The candidates can go through GMAT Quant practice papers to practice various types of questions to polish up their mathematical skills.

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