# CAT 2012 | Question: 18

947 views

A vessel has a milk solution in which milk and water are in the ratio $4:1$. By addition of water to it, milk solution with milk and water in the ratio $4:3$ was formed. On replacing $14\;\text{L}$ of this solution with pure milk the ratio of milk and water changed to $5:3$. What is the volume of the water added?

1. $12\;\text{L}$
2. $60\;\text{L}$
3. $32\;\text{L}$
4. $24\;\text{L}$

I got option C) 32L as the answer. Please correct me if I'm wrong.

60L
Initial ratio of milt to water $= 4:1$

So, if $4x$ amount of milk is there, $x$ amount of water is there.

Let $y$ be the amount of water added. Now, the ratio changes to $4:3.$ i.e., for $4x$ amount of milk, now there is $3x$ amount of water. So, we get that $y = 2x.$

In $14l,$ amount of water $= \frac{3}{3+4} \times14 = 6l$

Given, $\frac{4x+6}{3x-6} = \frac{5}{3}$

$\implies 12x + 18 = 15x -30$

$\implies x = 16$

$y = 2x = 32.$

## Related questions

In the figure given, $\text{OABC}$ is a parallelogram. The area of the parallelogram is $21$ sq units and the point $\text{C}$ lies on the line $x= 3$. Find the coordinat...
In the figure below, $\angle \text{MON} = \angle \text{MPO} = \angle \text{NQO} = 90^{\circ}$ and $\text{OQ}$ is the bisector of $\angle \text{MON}$ and $\text{QN} = 10,... 0 votes 1 answer 3 1,308 views Read the following information carefully and answer the question based on that. Two families are planning to go on a canoe trip together. The families consist of the foll... 0 votes 1 answer 4 472 views Fresh grapes contain$90\%$water by weight while dry grapes contain$20\%$water by weight. What is the weight of dry grapes available from$20$kg of fresh grapes?$2$k... 2 votes 1 answer 5 872 views A milkman mixes$20$litres of water with$80\$ litres of milk. After selling one-fourth of his mixture, he adds water to replenish the quantity that he has sold. What is ...