Question

A mixture of 30 liters of milk and water contains milk and water in the ratio 7:3 How much water must be added to it so that the ratio of the milk and water in the new mixture may be reversed?
A. 40 Litres
B. 35 Litres
C. 30 Litres
D. 25 Litres

Answer 1

Hint: The water added to get the reversed ratio in the original mixture can be calculated firstly calculating original composition of water and the milk. Later suppose the composition of water is x and write the milk to water ratio and equate it with the reversed ratio and find the value of x. To calculate the amount of water calculated can be calculated by subtracting the initial amount of water to the total amount of water.

Complete step-by-step answer:
It is given that the original mixture contains total 30 litres
And the milk to water ratio is given as \[7:3\]
Suppose the original mixture contains \[7x\] litres milk and \[3x\] litres of water
So \[7x + 3x = 30\]
Or,
 \[x = 3\]
So amount of milk = \[7 \times 3 = 21\] litres
Amount of water \[ = {\text{ }}3 \times 3 = 9\] litres
Not question says that the ratio should be reversed
so ratio of milk and water is \[3{\text{ }}:{\text{ }}7\] Since milk contents remain the same in both the mixtures
Suppose the amount of water is W litres
So \[21{\text{ }}:{\text{ }}W{\text{ }} = \;\;3{\text{ }}:{\text{ }}7\;\;i.e.{\text{ }}W{\text{ }} = {\text{ }}49\]
Hence water to be added in mixtures \[ = {\text{ }}49 - 9{\text{ }} = {\text{ }}40\] litres
So, the correct answer is “40 liters”.

Note: Here in this question it is asked that what is the amount of water should be added such that ratio will be in reversed order. So the added amount of water can be calculated by subtracting the initial amount of water to the total amount of water. So be careful while calculating the added amount of water.