Jar A and jar B, each have a mixture of milk and water. Quantity of milk in jar A is 180 litres and is three times the quantity of water in the same jar. Quantity of milk in jar B is twice that of water in the same jar. Contents of jar B was emptied into jar A, and as a result the respective ratio between the milk and water in the resultant mixture in jar A became 11:4. What is the initial quantity of milk in jar B? (in litres)

Options

A. 10
B. 60
C. 16
D. 40

Answer

To solve the problem step-by-step, we will analyze the information given and derive the necessary quantities.

### Step 1: Determine the quantity of water in Jar A
- We know that the quantity of milk in Jar A is 180 liters and that this quantity is three times the quantity of water in Jar A.
- Let the quantity of water in Jar A be \( W_A \).
- According to the problem, we have:
\[ 180 = 3 \times W_A \]
- Solving for \( W_A \):
\[ W_A = \frac{180}{3} = 60 \text{ liters} \]

### Step 2: Define the quantities in Jar B
- Let the quantity of water in Jar B be \( W_B \).
- The problem states that the quantity of milk in Jar B is twice that of water in Jar B.
- Therefore, the quantity of milk in Jar B, \( M_B \), can be expressed as:
\[ M_B = 2 \times W_B \]

### Step 3: Combine the contents of Jar A and Jar B
- When the contents of Jar B are emptied into Jar A, the total quantity of milk in Jar A becomes:
\[ M_A + M_B = 180 + 2W_B \]
- The total quantity of water in Jar A becomes:
\[ W_A + W_B = 60 + W_B \]

### Step 4: Set up the ratio of milk to water
- The resultant ratio of milk to water in Jar A after combining is given as 11:4.
- This can be expressed as:
\[ \frac{180 + 2W_B}{60 + W_B} = \frac{11}{4} \]

### Step 5: Cross-multiply to eliminate the fraction
- Cross-multiplying gives us:
\[ 4(180 + 2W_B) = 11(60 + W_B) \]
- Expanding both sides:
\[ 720 + 8W_B = 660 + 11W_B \]

### Step 6: Rearranging the equation
- Rearranging the equation to isolate \( W_B \):
\[ 720 - 660 = 11W_B - 8W_B \]
\[ 60 = 3W_B \]
- Solving for \( W_B \):
\[ W_B = \frac{60}{3} = 20 \text{ liters} \]

### Step 7: Calculate the initial quantity of milk in Jar B
- Now that we have \( W_B \), we can find the quantity of milk in Jar B:
\[ M_B = 2 \times W_B = 2 \times 20 = 40 \text{ liters} \]

### Final Answer
The initial quantity of milk in Jar B is **40 liters**.

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