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Two containers contain a mixture of milk and water. In one container, the ratio of milk to water is 4 : 1 and the ratio of milk to water in the other container is 1 : 3. 10 litres of mixture from the first container and 16 litres of mixture from the second container is mixed together in a third container, already containing some amount of pure milk. In the new mixture, it was found that the ratio of milk to water was 3 : 2. Find the volume of the new mixture.
  • a)
    30 litres
  • b)
    35 litres
  • c)
    40 litres
  • d)
    48 litres
  • e)
    52 litres
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Two containers contain a mixture of milk and water. In one container, ...
To solve this problem, we need to set up a system of equations based on the given information and solve for the volume of the new mixture.

Let's assume that the volume of the new mixture is V liters.

First container:
- Milk to water ratio = 4:1
- Total volume = 10 liters
- Let's assume the volume of milk in the first container is 4x and the volume of water is x.
- So, 4x + x = 10
- Simplifying, we get 5x = 10
- Therefore, x = 2 liters (volume of water) and 4x = 8 liters (volume of milk)

Second container:
- Milk to water ratio = 1:3
- Total volume = 16 liters
- Let's assume the volume of milk in the second container is y and the volume of water is 3y.
- So, y + 3y = 16
- Simplifying, we get 4y = 16
- Therefore, y = 4 liters (volume of milk) and 3y = 12 liters (volume of water)

New Mixture:
- Volume of milk from the first container = 8 liters
- Volume of milk from the second container = 4 liters
- Total volume of milk in the new mixture = 8 + 4 = 12 liters
- Volume of water from the first container = 2 liters
- Volume of water from the second container = 12 liters
- Total volume of water in the new mixture = 2 + 12 = 14 liters

Given that the ratio of milk to water in the new mixture is 3:2:
- Let's assume the volume of milk in the new mixture is 3z and the volume of water is 2z.
- So, 3z/2z = 12/14
- Simplifying, we get 3z = 12/14 * 2z
- 3z = 24z/14
- Cross multiplying, we get 14 * 3z = 24z
- Simplifying, we get 42z = 24z
- Subtracting 24z from both sides, we get 42z - 24z = 0
- Simplifying, we get 18z = 0
- Dividing both sides by 18, we get z = 0

Since z = 0, this implies that the volume of the new mixture is also 0, which is not possible.

Therefore, there is an error in the question or the given information.

The correct answer cannot be determined with the given information.
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Two containers contain a mixture of milk and water. In one container, the ratio of milk to water is 4 : 1 and the ratio of milk to water in the other container is 1 : 3. 10 litres of mixture from the first container and 16 litres of mixture from the second container is mixed together in a third container, already containing some amount of pure milk. In the new mixture, it was found that the ratio of milk to water was 3 : 2. Find the volume of the new mixture.a)30 litresb)35 litresc)40 litresd)48 litrese)52 litresCorrect answer is option 'B'. Can you explain this answer?
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