A container has 60 liters of a mixture of milk and water in the ratio of 2:1. If

What’s inside this PDF?

Question: A container has 60 liters of a mixture of milk and water in the ratio of 2:1. If 12 liters of the mixture is replaced with water, what is the new ratio of milk to water?

Options:

2:1
1:2
1:1
3:2

Correct Answer: 3:2

Solution:

Initially, milk = 40 liters, water = 20 liters. After removing 12 liters (8 liters milk and 4 liters water), we have 32 liters milk and 16 liters water. Adding 12 liters of water gives 32 liters milk and 28 liters water, resulting in a ratio of 32:28 or 8:7.

Practice Questions

Q1

A container has 60 liters of a mixture of milk and water in the ratio of 2:1. If 12 liters of the mixture is replaced with water, what is the new ratio of milk to water?

2:1
1:2
1:1
3:2

Questions & Step-by-Step Solutions

A container has 60 liters of a mixture of milk and water in the ratio of 2:1. If 12 liters of the mixture is replaced with water, what is the new ratio of milk to water?

Step 1: Understand the initial mixture. The container has 60 liters of a mixture of milk and water in the ratio of 2:1.
Step 2: Calculate the amount of milk and water in the initial mixture. Since the ratio is 2:1, for every 3 parts of the mixture, 2 parts are milk and 1 part is water.
Step 3: Calculate the total parts in the mixture. 2 parts (milk) + 1 part (water) = 3 parts.
Step 4: Find the amount of milk. (2/3) * 60 liters = 40 liters of milk.
Step 5: Find the amount of water. (1/3) * 60 liters = 20 liters of water.
Step 6: Now, we need to replace 12 liters of the mixture with water. First, we find out how much milk and water is in those 12 liters.
Step 7: Calculate the amount of milk in 12 liters. Since the ratio is 2:1, in 12 liters, there are (2/3) * 12 = 8 liters of milk.
Step 8: Calculate the amount of water in 12 liters. In 12 liters, there are (1/3) * 12 = 4 liters of water.
Step 9: Remove 12 liters from the mixture. After removing, we have 40 liters of milk - 8 liters = 32 liters of milk and 20 liters of water - 4 liters = 16 liters of water.
Step 10: Now, add 12 liters of water to the remaining mixture. So, we have 32 liters of milk and 16 liters of water + 12 liters of water = 28 liters of water.
Step 11: Finally, find the new ratio of milk to water. The new ratio is 32 liters of milk to 28 liters of water.
Step 12: Simplify the ratio 32:28. Divide both numbers by 4 to get 8:7.

Ratio and Proportion – Understanding how to calculate and manipulate ratios in mixtures.
Mixture Problems – Applying concepts of mixtures to determine the composition after changes.
Substitution – Replacing part of a mixture and calculating the new composition.

A container has 60 liters of a mixture of milk and water in the ratio of 2:1. If

What’s inside this PDF?

A container has 60 liters of a mixture of milk and water in the ratio of 2:1. If

Practice Questions

Questions & Step-by-Step Solutions

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?