Question: Two vessels A and B contain spirit and water mixed in the ratio 5:2 and 7:6 respectively. Find the ratio in which this mixture be mixed to obtain a new mixture in vessel c containing spirit and water in the ratio 8:5?

1. 1:7
2. 2:9
3. 3:8
4. 7:9
5. 8:9

Correct Answer: D
Solution and Explanation:
Approach Solution 1:

The problem statement states that:
Given:

• Two vessels A and B contain spirit and water mixed in the ratio of 5:2 and 7:6 respectively.

Find Out:

• The ratio in which this mixture is mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8:5.

A ratio reflects a part to part relation. In this case, we need to find out the ratio of spirit to water.

The total of one entity whose elements are reflected in a ratio is the sum of both these entities.

Volume of Spirit in Vessel A = 5/ (5+2) *x
=> Volume of Spirit in Vessel A = 5/7x……. (1)

Volume of Spirit in Vessel B = 7/ (7+6) *y
=> Volume of Spirit in Vessel B = 7/13y……. (2)

Volume of Spirit in Vessel C = 8/ (8+5) *[x+y]
=> Volume of Spirit in Vessel C = 8/13 [x+y]

To get the volume of spirit in vessel C we need to add the equations (1) and (2) –

Volume of Spirit in Vessel C = 5/7x + 7/13y

Therefore, we can say:
=> 8/13 [x+y] = 5/7x +7/13y
=> 8/13x + 8/13y = 5/7x +7/13 y
=> 8/13y – 7/13y = 5/7x – 8/13x
=> 1/13y = [65 – 56]/91x
=> 1/13y = 9/91x
=> y = 9/91x * 13
=> y = 9/7x
So, y/x = 9/7 and x/y = 7/9 or x : y = 7 : 9

The mixture in vessel A and B need to be mixed in the ratio of 7:9 to obtain a new mixture in vessel C containing spirit and water in the ratio of 8:5.

Approach Solution 2:

The problem statement informs that:
Given:

• Two vessels A and B contain spirit and water mixed in the ratio of 5:2 and 7:6 respectively.

Find Out:

• The ratio in which this mixture is mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8:5.

Vessel C contains a ratio of spirit and water being 8:5
This implies that the total volume of contents in the vessel is 8+5 = 13 units

The contents of vessel C are made up of mixing the contents from Vessel A & B.
Let’s assume that:
Contribution of vessel A = a litres
Contribution of vessel B = b litres

Total volume of vessel C’s contents = X litres
So, X = a + b ……. (1)
Therefore, the total volume of spirit in vessel C = 8/13X litres
Total Volume of Spirit that Vessel A contributed to Vessel C = 5/7a
Total Volume of Spirit that Vessel B contributed to Vessel C = 7/13b
Total Volume of Spirit in Vessel C = 8/13X

Now, total volume of spirit in Vessel C is equal to the sum of the spirit from Vessels A & B.
So, 8/13X = 5/7a + 7/13b

From Equation (1) we know that X = a + b
By plugging the value of X in the equation we get:
=> 8/13 [a+b] = 5/7a + 7/13b
=> 8/13a + 8/13b = 5/7a + 7/13b
=> 8/13b – 7/13b = 5/7a – 8/13a
=> 1/13b = [65 – 56]/91a
=> b = 9/91a * 13
=> b = 9/7a
=> b/a = 9/7 or a/b = 7/9.
So, a:b = 7:9

Hence, the mixture in vessel A and B need to be mixed in the ratio of 7:9 to obtain a new mixture in vessel C containing spirit and water in the ratio of 8:5.

Approach Solution 3:

The problem statement implies that:
Given:

• Two vessels A and B contain spirit and water mixed in the ratio of 5:2 and 7:6 respectively.

Find Out:

• The ratio in which this mixture is mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8:5.

Ratio of Spirit and Water in Vessel A = 5:2
So, Spirit in one Litre mix from Vessel A = 5/7 litre……(1)
Ratio of Spirit and Water in Vessel B = 7:6
So, Spirit in one Litre mix from Vessel B = 7/13 litre………(2)
Ratio of Spirit and Water in Vessel C = 8:5
So, Spirit in one litre mix from Vessel C = 8/13 litre ………..(3)

Using Alligation,

Therefore, A : B = 7 : 9

Hence, the mixture in vessel A and B need to be mixed in the ratio of 7:9 to obtain a new mixture in vessel C containing spirit and water in the ratio of 8:5.

“Two vessels A and B contain spirit and water mixed in the ratio 5:2”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. To solve the GMAT Problem Solving questions, the candidates must have a concrete knowledge of arithmetic, algebra and geometry. The candidates can analyse GMAT Quant practice papers to go through different types of questions that will enable them to improve their mathematical learning.

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