Question

In 40 liters of milk and water the ratio of milk and water is 3:1. How much water should be added in the mixture so that the ratio of milk to water becomes 2:1

(A) 8
(B) 6
(C) 5
(D) 4
(E) 3

Answer 1

To adjust the ratio of milk to water from 3:1 to 2:1 in a 40-liter mixture, 5 additional liters of water are required to be added to the current 10 liters of water, bringing the total to 15 liters to match the 30 liters of milk.

Step-by-step explanation:

In a mixture of 40 liters of milk and water with a ratio of 3:1, there are 30 liters of milk and 10 liters of water. To change the ratio to 2:1, the amount of milk must be twice the amount of water. As there are currently 30 liters of milk, we need a total of 15 liters of water to make the ratio 2:1. Since there is already 10 liters of water in the mixture, we need to add 5 liters of water.

Here's the step-by-step calculation:

1. Original water in mixture: Total volume × (1 part / (3 parts + 1 part)) = 40 liters × 1/4 = 10 liters.
2. Original milk in mixture: Total volume - Original water in mixture = 40 liters - 10 liters = 30 liters.
3. Desired ratio of milk to water = 2:1, meaning for every 2 liters of milk, there must be 1 liter of water.
4. To find the needed water for the new ratio, divide the amount of milk by 2 to get 30 liters / 2 = 15 liters.
5. Additional water required = Desired total water - Original water in mixture = 15 liters - 10 liters = 5 liters.