Sony has a certain quantity of mixture in her bottle containing water and milk in the ratio 3 : 5. respectively. She takes out some quantity of that mixture and replaces it with an equal quantity of water. If the ratio of water to the milk in the new mixture is x : y , then select the INCORRECT statement from the following options .

In this question, we need to check with each option.

A) If 1/6 part of the mixture is replaced with water.

The initial part of the water is 3/8, and that of milk is 5/8. When 1/6 of the mixture is replaced with water, the milk taken out will be added as water. $$\frac{1}{6}\cdot\frac{5}{8}=\frac{5}{48}$$ is the amount of milk that is taken out, and that will also be the amount of water added.

So, the new ratio will be $$\frac{x}{y}=\frac{\left(\frac{3}{8}+\frac{5}{48}\right)}{\frac{5}{8}-\frac{5}{48}}=\frac{23}{25}$$. But in the option it is given that x>y. So, it is the incorrect option.

B) If $$\frac{1}{5}$$, part of the mixture is replaced with water.

The initial part of the water is 3/8, and that of milk is 5/8. When 1/5 of the mixture is replaced with water, the milk taken out will be added as water. $$\frac{1}{5}\cdot\frac{5}{8}=\frac{1}{8}$$ is the amount of milk that is taken out, and that will also be the amount of water added.

So, the new ratio will be $$\frac{x}{y}=\frac{\left(\frac{3}{8}+\frac{1}{8}\right)}{\frac{5}{8}-\frac{1}{8}}=\frac{\left(\frac{4}{8}\right)}{\left(\frac{4}{8}\right)}=1:1$$. In the option it is given that x=y. So, it is a correct option.

C) If $$\frac{1}{7}$$, part of the mixture is replaced with water.

The initial part of the water is 3/8, and that of milk is 5/8. When 1/7 of the mixture is replaced with water, the milk taken out will be added as water. $$\frac{1}{7}\cdot\frac{5}{8}=\frac{5}{56}$$ is the amount of milk that is taken out, and that will also be the amount of water added.

So, the new ratio will be $$\frac{x}{y}=\frac{\left(\frac{3}{8}+\frac{5}{56}\right)}{\frac{5}{8}-\frac{5}{56}}=\frac{26}{30}$$. In the option it is given that xy. So, it is a correct option.

D) If $$\frac{1}{4}$$, part of the mixture is replaced with water.

The initial part of the water is 3/8, and that of milk is 5/8. When 1/4 of the mixture is replaced with water, the milk taken out will be added as water. $$\frac{1}{4}\cdot\frac{5}{8}=\frac{5}{32}$$ is the amount of milk that is taken out, and that will also be the amount of water added.
So, the new ratio will be $$\frac{x}{y}=\frac{\left(\frac{3}{8}+\frac{5}{32}\right)}{\frac{5}{8}-\frac{5}{32}}=\frac{17}{15}$$. In the option it is given that x>y. So, it is a correct option.