# In a mixture of \[35\] litres, the ratio of milk to water is \[4:1\]. If \[7\] litres of water are added to the mixture, find the ratio of milk and water in the resulting mixture.

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Hint: Convert the given ratios into equations by taking the ratios in variable form. This method helps to find the new ratio of the resulting mixture of added or removed quantity of milk or water.

Given total mixture \[ = 35l\]

Let \[x\] parts are dividing the ratio of milk to water

Then, Quantity of milk \[ = 4x\]

Quantity of water \[ = x\]

So, Quantity of the total mixture \[ = 4x + x = 5x\] which is equal to \[35l\]

i.e., \[5x = 35l\]

\[\therefore x = 7l\] and \[4x = 4 \times 7 = 28l\]

If \[7\]litres of water are added to the mixture then,

Quantity of milk \[ = 4x = 28l\]

Quantity of water \[ = 7 + 7 = 14l\]

So, the ratio of the resulting mixture of milk to water is given by \[28l:14l = 2:1\]

Therefore, the ratio of milk to water in the resulting mixture is \[2:1\].

Note: In these types of questions sometimes they ask for the value of the problem. So, the value of the problem is “By adding the water to the resulting mixture decreases the ratio of milk to water i.e. the quality of milk has been reduced.”

Given total mixture \[ = 35l\]

Let \[x\] parts are dividing the ratio of milk to water

Then, Quantity of milk \[ = 4x\]

Quantity of water \[ = x\]

So, Quantity of the total mixture \[ = 4x + x = 5x\] which is equal to \[35l\]

i.e., \[5x = 35l\]

\[\therefore x = 7l\] and \[4x = 4 \times 7 = 28l\]

If \[7\]litres of water are added to the mixture then,

Quantity of milk \[ = 4x = 28l\]

Quantity of water \[ = 7 + 7 = 14l\]

So, the ratio of the resulting mixture of milk to water is given by \[28l:14l = 2:1\]

Therefore, the ratio of milk to water in the resulting mixture is \[2:1\].

Note: In these types of questions sometimes they ask for the value of the problem. So, the value of the problem is “By adding the water to the resulting mixture decreases the ratio of milk to water i.e. the quality of milk has been reduced.”

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