A 24 litres of milk and water mixture contains milk and water in the ratio 3 : 5. what litres of the mixture should be taken out and replaced with pure milk so that the final mixture contains milk and water in equal proportions?
Answers
Now since the mixture is to be replaced with pure milk, the amount of mixture will remain same after replacement too.
In 24 l mixture, to have 12 l water and 12 l milk, 3 l of water should be taken out, since we are only adding milk.
Let x l of mixture taken out. So 5/8 * x = 3,
Solve, x = 24/5 l
Answer:
Step-by-step explanation:
There is a 24 Liters mixture of Milk and Water and the proportion of Milk to Water is 3 : 5. This means that there’s 3 L of Milk and 5 L of Water per 3+5 = 8 L of Mixture. Therefore, in 24 L Mixture, there’s 9 L Milk and 15 L Water (9+15 = 24).
Currently there’s 15 L of Water and the Water has to come down to 12 L, so that the final Mixture (after adding equal amount of Milk) would contain 12 L Water and 12 L Milk. If we remove 4.8 L of Mixture it would mean that we are removing 1.8 L Milk and 3 L Water, because 1.8 : 3 is nothing but 3 : 5 (1.8*5 = 3*3).
As we remove 4.8 L of Mixture from 24 L of Mixture, the remaining Mixture is 19.2 L and this contains 7.2 L Milk and 12 L Water, as 7.2 : 12 is same as 3 : 5 (7.2*5 = 12*3).
We have removed 4.8 L of Mixture and as we finally add 4.8 L of Milk, we come back to 7.2 + 4.8 = 12 L Milk and 12 L Water thus taking it to equal proportion.
Thus, out of 24 L of original Mixture (Milk : Water is 3 : 5), we need to take away 4.8 L Mixture and add 4.8 L Milk so that the final Mixture would contain Milk and Water in equal proportions.