A Chemist Mixes Two Liquids 1 and 2. One Litre of Liquid 1 Weighs 1 Kg GMAT Problem Solving

Question: A chemist mixes two liquids 1 and 2. One litre of liquid 1 weighs 1 kg and one litre of liquid 2 weighs 800 gm. If half litre of the mixture weighs 480 gm, then the percentage of liquid 1 in the mixture, in terms of volume, is

1. 70
2. 75
3. 80
4. 85
5. 90

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

The problem statement states that:
Given:

• A chemist mixes two liquids 1 and 2.
• One litre of liquid 1 weighs 1 kg and one litre of liquid 2 weighs 800 gm.
• Half litre of the mixture weighs 480 gm

Find out:

• The percentage of liquid 1 in the mixture in terms of volume.

1 L of liquid 1 weighs 1.0 kg
1 L of liquid 2 weighs 800 gm = 800/1000 = 0.8 kg
Since ½ L of mixture weighs 480 gm, 1 L of mixture weighs = 2 * 480/1000
= 2 * 0.48
= 0.96 kg

Let, a% of liquid 1 and (100 – a)% of liquid 2 is there in the mixture in terms of volume

Therefore, we can say:
0.96 = (1) * a/100 + {(0.8) * (100-a)}/100
=> 96 = a + 80 - 0.8a
=> 16 = 0.2a
=> a% = 80%

Hence, the percentage of liquid 1 in the mixture, in terms of volume, is 80%

Approach Solution 2:

The problem statement informs that:
Given:

• A chemist mixes two liquids 1 and 2.
• One litre of liquid 1 weighs 1 kg and one litre of liquid 2 weighs 800 gm.
• Half litre of the mixture weighs 480 gm

Find out:

• The percentage of liquid 1 in the mixture in terms of volume.

One litre of liquid 1 weighs = 1 kg = 1000 gm
One litre of liquid 2 weighs = 800 gm
Half of liquid 1 will be 500 gms
Half of liquid 2 will be 400 gms
Half litre of the mixture weighs 480 gm
By using alligation method, we get
----500 —---- 400
---- —- 480----
-----80-------20

ratio of liquid 1 to liquid 2 = 4 : 1
The percentage of liquid 1 in the mixture in terms of volume= 4/5 * 100 = 80.

Approach Solution 3:

The problem statement implies that:
Given:

• A chemist mixes two liquids 1 and 2.
• One litre of liquid 1 weighs 1 kg and one litre of liquid 2 weighs 800 gm.
• Half litre of the mixture weighs 480 gm

Asked:

• To find out the percentage of liquid 1 in the mixture in terms of volume.

The question is experimenting with the concept of weighted average with two liquids of different concentrations.

Concentration of Liquid 1 = 1kg/1Litre = 1000g/1000ml = 1 g/ml
Concentration of Liquid 2 = 800g/1Litre = 800g/1000ml = 0.8 g/ml

Half litre of the mixture weighs 480 g
Final concentration (weighted average) in 1 litre of final solution = 0.480 * 2 = 0.960 g/ml

Let volume of liquid 1 mixed = a
Let volume of liquid 2 mixed = b
Therefore, Percentage of liquid 1 = a/a+b ∗100

As per weighted average concept = (1∗a + 0.8∗b) / a + b = 0.96
=> a/b =4

Hence, a/a+b ∗100 = 4/5 ∗100 = 80%

Therefore, the percentage of liquid 1 in the mixture, in terms of volume, is 80%

“A chemist mixes two liquids 1 and 2. One litre of liquid 1 weighs 1 kg”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. The candidates must access information in order to solve the GMAT Problem Solving questions. The candidates need to practice more questions from the GMAT Quant practice papers to improve their mathematical knowledge and understanding.

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