To make a certain profit, a milkman mixes 30 liters of water in 120 liters of milk. He adds up water to the mixture, after selling one third of it, in order to make up the loss. What is the water to milk ratio at the moment?

a. 3:7
b. 4:9
c. 6:11
d. 7:12

To solve this, let’s break down the problem:

1. **Initial Mixture**:
   - The milkman starts with 120 liters of milk and 30 liters of water.
   - Total volume of the mixture = \(120 + 30 = 150\) liters.
   
2. **Mixture Sold**:
   - He sells one-third of the total mixture, which is \( \frac{1}{3} \times 150 = 50 \) liters.
   - The 50 liters sold will contain both milk and water in the same ratio as the original mixture.

   The initial milk-to-water ratio is:
   \[
   \frac{120}{30} = 4:1
   \]

3. **Amount of Milk and Water in 50 Liters Sold**:
   - Water in the 50 liters = \( \frac{1}{5} \times 50 = 10 \) liters
   - Milk in the 50 liters = \( \frac{4}{5} \times 50 = 40 \) liters

4. **Remaining Mixture**:
   - After selling 50 liters, he has:
     - Water: \(30 - 10 = 20\) liters
     - Milk: \(120 - 40 = 80\) liters
   - Remaining mixture = \(80 + 20 = 100\) liters.

5. **Adding Water to Compensate**:
   - He adds water to bring the mixture back to the original total volume of 150 liters.
   - Required amount of water to add = \(150 - 100 = 50\) liters.

6. **Final Mixture Composition**:
   - Total water = \(20 + 50 = 70\) liters
   - Total milk = 80 liters

7. **Final Ratio of Water to Milk**:
   \[
   \text{Water : Milk} = 70 : 80 = 7 : 8
   \]

Thus, the correct answer is not in the options given.

If any questions or details needed?  
Here are 5 questions to expand understanding:
1. How to calculate the proportion of substances when the ratio is given?
2. Why did the milk and water ratio remain the same in each fraction of the mixture sold?
3. What other ways could the milkman adjust the mixture to compensate for the water?
4. How can we determine the final ratios when scaling quantities up or down?
5. In what real-life situations are these mixture ratio calculations applicable?

**Tip:** Always verify the volume of individual components before and after operations in mixture problems for accuracy.

Explore how to calculate the final water-to-milk ratio after the milkman sells one-third of a milk-water mixture and replenishes the loss with water. This example involves the concepts of ratio conservation, mixture and alligation, and proportional removal. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation