A drum of 20 litres is filled with milk. A milkman has only two measuring vessels of 3 litres and 5 litres without any calibration. He has to measure four litres of milk for a customer without using anyother vessel. Minimum how many operations are required for this work, where an operation is counted if the milk is transferred from one vessel to another vessel?

Options

A. a. 5
B. b. 6
C. c. 8
D. d. 11

Answer

To solve the problem of measuring 4 liters of milk using a 3-liter and a 5-liter vessel, we can follow these steps:

### Step-by-Step Solution:

1. **Fill the 5-liter vessel from the drum.**
- **Operation 1:** Fill the 5-liter vessel completely from the drum.
- **Current state:** 5 liters in the 5-liter vessel, 0 liters in the 3-liter vessel.

2. **Pour from the 5-liter vessel into the 3-liter vessel.**
- **Operation 2:** Pour 3 liters from the 5-liter vessel into the 3-liter vessel.
- **Current state:** 2 liters remain in the 5-liter vessel (5 - 3 = 2), and the 3-liter vessel is now full (3 liters).

3. **Empty the 3-liter vessel.**
- **Operation 3:** Empty the 3-liter vessel back into the drum.
- **Current state:** 2 liters in the 5-liter vessel, 0 liters in the 3-liter vessel.

4. **Pour the remaining 2 liters from the 5-liter vessel into the 3-liter vessel.**
- **Operation 4:** Pour the 2 liters from the 5-liter vessel into the 3-liter vessel.
- **Current state:** 0 liters in the 5-liter vessel, and 2 liters in the 3-liter vessel.

5. **Fill the 5-liter vessel again from the drum.**
- **Operation 5:** Fill the 5-liter vessel completely from the drum.
- **Current state:** 5 liters in the 5-liter vessel, 2 liters in the 3-liter vessel.

6. **Pour from the 5-liter vessel into the 3-liter vessel until the 3-liter vessel is full.**
- **Operation 6:** Pour from the 5-liter vessel into the 3-liter vessel. Since the 3-liter vessel already has 2 liters, it can only take 1 more liter.
- **Current state:** 4 liters in the 3-liter vessel (2 + 1 = 3), and 4 liters remain in the 5-liter vessel (5 - 1 = 4).

Now, we have successfully measured 4 liters of milk in the 3-liter vessel.

### Summary of Operations:
- Total operations required: **6**