Question

A mixture contains alcohol and water in the ratio 4:3. If 5 litres of water is added to the mixture, the ratio becomes 4:5. Find the quantity of alcohol in the given mixture.
A) 5 Ltr
B) 7.5 Ltr
C) 10 Ltr
D) 12 Ltr

Answer 1

Hint:
If we interpret the ratio, we get 3x litres of water and 4x litres of alcohol present. Let us take the amount of mixture taken out to be 7p litres. The amount of water and alcohol contained in the new mixture is in the ratio 4:5, that is if 4 parts of alcohol, 5 parts of water. As the quantity of alcohol has not changed so we will use that value to calculate the quantity of water and then alcohol.

Complete step by step solution:
It is given a mixture of alcohol and water in the ratio 4: 3.
So, we can say that the amount of alcohol is 4x and the amount of water is 3x.
So, the total quantity of mixture present is 7x.
Now we will add 5 litres of water to the mixture so amount of water in the new mixtures becomes 3x + 5
So that the ratio of alcohol and water in the resultant mixture becomes 4 : 5.
So, we can say that the amount of alcohol is 4y and the amount of water is 5y in the resultant mixture.
So, the total quantity of mixture present is 9y in the resultant mixture.
As we know the quantity of alcohol has not changed. So, we get
$ \Rightarrow 4x = 4y \Rightarrow x = y$
As we know the difference between the quantity of water in two mixtures is 5 litres.
$ \Rightarrow 5y = 3x + 5$
But we know $x = y$, so by substituting the value of y in the equation, we get
$ \Rightarrow 5x = 3x + 5$
$ \Rightarrow x = \dfrac{5}{2}$
Now to find the amount of alcohol, we will multiply the value of x by 4.
$ \Rightarrow 4x = 4\left( {\dfrac{5}{2}} \right) = 10$
So, the quantity of alcohol in the given mixture is 10 ltr.

Hence, the correct answer to the above question is option (C).

Note:
The things to be pointed out is: as some amount of water is added, the total quantity of the mixture has also changed by the same quantity. The other thing to keep in mind is that the quantity of water which is being added will change the composition of the whole mixture.