A container is filled with the mixture of milk and water. The ratio of milk and water is same. Bobby and Sunny increases the concentration of 60%. Bobby makes it by adding the milk and Sunny makes it by replacing the mixture with milk. What is the percentage of milk added by Bobby to that of milk replaced by Sunny:

Options

A. a. 1
B. b. 1.2
C. c. 1.3333
D. d. None of these

Answer

To solve the problem, we need to analyze the actions of Bobby and Sunny in terms of the milk and water mixture and how they change the concentration of milk in the container.

### Step-by-Step Solution:

1. **Understand the Initial Mixture**:
- The initial ratio of milk to water is 1:1.
- Let's assume the total volume of the mixture is \(2x\) liters, where \(x\) liters is milk and \(x\) liters is water.

2. **Determine the Initial Concentration**:
- The initial concentration of milk in the mixture is:
\[ \text{Concentration of milk} = \frac{x}{2x} = \frac{1}{2} = 50\% \]

3. **Target Concentration**:
- Both Bobby and Sunny aim to increase the concentration of milk to 60%.

4. **Bobby's Method**:
- Bobby adds milk to the mixture. Let the amount of milk added by Bobby be \(a\) liters.
- After adding \(a\) liters of milk, the new volume of milk becomes \(x + a\) liters.
- The total volume of the mixture remains \(2x\) liters.
- The new concentration of milk after Bobby's addition is:
\[ \frac{x + a}{2x} = 0.6 \]
- Solving for \(a\):
\[ x + a = 0.6 \times 2x \]
\[ x + a = 1.2x \]
\[ a = 1.2x - x = 0.2x \]

5. **Sunny's Method**:
- Sunny replaces part of the mixture with milk. Let the amount of mixture replaced be \(b\) liters.
- Since he is replacing the mixture, the amount of milk in the replaced mixture is \(\frac{x}{2}\) liters (because the mixture is 50% milk).
- After replacing \(b\) liters of the mixture with \(b\) liters of milk, the new amount of milk becomes:
\[ x - \frac{b}{2} + b = x + \frac{b}{2} \]
- The total volume of the mixture remains \(2x\) liters.
- The new concentration of milk after Sunny's replacement is:
\[ \frac{x + \frac{b}{2}}{2x} = 0.6 \]
- Solving for \(b\):
\[ x + \frac{b}{2} = 0.6 \times 2x \]
\[ x + \frac{b}{2} = 1.2x \]
\[ \frac{b}{2} = 1.2x - x = 0.2x \]
\[ b = 0.4x \]

6. **Calculate the Percentage of Milk Added by Bobby to Milk Replaced by Sunny**:
- Bobby added \(a = 0.2x\) liters of milk.
- Sunny replaced \(b = 0.4x\) liters of milk.
- The percentage of milk added by Bobby compared to the milk replaced by Sunny is:
\[ \text{Percentage} = \left( \frac{a}{b} \right) \times 100 = \left( \frac{0.2x}{0.4x} \right) \times 100 = 50\% \]

### Final Answer:
The percentage of milk added by Bobby to that of milk replaced by Sunny is **50%**.