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A jar full of milk contains 30% water. A part of this milk is replaced by containing 20% water and now the percentage of water is found to be 26%. The quantity of milk replaced is Options :2/51/53/74/7

Question

A jar full of milk contains 30% water. A part of this milk is replaced by containing 20% water and now the percentage of water is found to be 26%. The quantity of milk replaced is Options :2/51/53/74/7

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Solution 1

This problem can be solved using the concept of mixtures and allegations. Here are the steps:

  1. The initial mixture in the jar has 30% water.
  2. A part of this mixture is replaced with another mixture that has 20% water.
  3. After the replacement, the new mixture in the jar has 26% water.

We can use the rule of allegation which states that:

(Quantity of cheaper/Quantity of dearer) = (CP of dearer - Mean Price)/(Mean Price - CP of cheaper)

Here, the 'cheaper' mixture is the one with 20% water and the 'dearer' mixture is the one with 30% water. The mean price is the percentage of water in the final mixture, which is 26%.

So, we substitute these values into the formula:

(Quantity of cheaper/Quantity of dearer) = (30 - 26)/(26 - 20)
(Quantity of cheaper/Quantity of dearer) = 4/6 = 2/3

This means that 2/3 of the mixture was replaced. So, the answer is 2/3. However, this option is not available in the given options. There might be a mistake in the problem or the options provided.

This problem has been solved

Solution 2

This problem can be solved using the concept of mixtures and allegations. Here are the steps:

  1. The initial mixture in the jar has 30% water.
  2. A part of this mixture is replaced by another mixture containing 20% water.
  3. After the replacement, the new mixture in the jar has 26% water.

We can use the rule of allegation which states that:

(Quantity of cheaper/Quantity of dearer) = (CP of dearer - Mean Price)/(Mean Price - CP of cheaper)

Here, the 'cheaper' mixture is the one with 20% water and the 'dearer' mixture is the one with 30% water. The mean price is the final percentage of water, which is 26%.

So, we substitute these values into the formula:

(Quantity of cheaper/Quantity of dearer) = (30 - 26)/(26 - 20)
(Quantity of cheaper/Quantity of dearer) = 4/6 = 2/3

This means that 2/3 of the mixture was replaced, so the answer is 2/3. However, this option is not available in the given options. There might be a mistake in the problem or the options provided.

This problem has been solved

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