5 litres of honey contains 80% sugar. 3 litres of water is added to this honey. What is the per centage of sugar in the new mixture?

Options

A. 40
B. 50
C. 60
D. 75

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the amount of sugar in the honey
Given that 5 liters of honey contains 80% sugar, we can calculate the amount of sugar in the honey.

\[ \text{Amount of sugar} = \text{Total volume of honey} \times \text{Percentage of sugar} \]
\[ \text{Amount of sugar} = 5 \, \text{liters} \times 0.80 = 4 \, \text{liters} \]

### Step 2: Calculate the amount of water in the honey
Since the honey is 80% sugar, the remaining percentage is water. Therefore, we can calculate the amount of water in the honey.

\[ \text{Amount of water in honey} = \text{Total volume of honey} - \text{Amount of sugar} \]
\[ \text{Amount of water in honey} = 5 \, \text{liters} - 4 \, \text{liters} = 1 \, \text{liter} \]

### Step 3: Add the additional water
Now, we add 3 liters of water to the existing 1 liter of water in the honey.

\[ \text{Total amount of water} = \text{Water in honey} + \text{Additional water} \]
\[ \text{Total amount of water} = 1 \, \text{liter} + 3 \, \text{liters} = 4 \, \text{liters} \]

### Step 4: Calculate the total volume of the new mixture
Now, we can find the total volume of the new mixture, which consists of the honey and the added water.

\[ \text{Total volume of mixture} = \text{Volume of honey} + \text{Total amount of water} \]
\[ \text{Total volume of mixture} = 5 \, \text{liters} + 3 \, \text{liters} = 8 \, \text{liters} \]

### Step 5: Calculate the percentage of sugar in the new mixture
Now, we can calculate the percentage of sugar in the new mixture.

\[ \text{Percentage of sugar} = \left( \frac{\text{Amount of sugar}}{\text{Total volume of mixture}} \right) \times 100 \]
\[ \text{Percentage of sugar} = \left( \frac{4 \, \text{liters}}{8 \, \text{liters}} \right) \times 100 = 50\% \]

### Final Answer
The percentage of sugar in the new mixture is **50%**.

---