A sugar solution of 3 litres contains 40% sugar. One litre of water is added to this solution. What is the percentage of sugar in the new solution ?

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the amount of sugar in the original solution.
The original solution is 3 liters and contains 40% sugar.

\[ \text{Amount of sugar} = \text{Total volume} \times \left(\frac{\text{Percentage of sugar}}{100}\right) \]

\[ \text{Amount of sugar} = 3 \, \text{liters} \times \left(\frac{40}{100}\right) = 3 \times 0.4 = 1.2 \, \text{liters} \]

### Step 2: Calculate the amount of water in the original solution.
The total volume of the solution is 3 liters, and we have already calculated that there are 1.2 liters of sugar.

\[ \text{Amount of water} = \text{Total volume} - \text{Amount of sugar} \]

\[ \text{Amount of water} = 3 \, \text{liters} - 1.2 \, \text{liters} = 1.8 \, \text{liters} \]

### Step 3: Add 1 liter of water to the solution.
Now, we need to add 1 liter of water to the existing amount of water.

\[ \text{New amount of water} = \text{Original amount of water} + 1 \, \text{liter} \]

\[ \text{New amount of water} = 1.8 \, \text{liters} + 1 \, \text{liter} = 2.8 \, \text{liters} \]

### Step 4: Calculate the total volume of the new solution.
The total volume of the new solution is the sum of the amount of sugar and the new amount of water.

\[ \text{Total volume of new solution} = \text{Amount of sugar} + \text{New amount of water} \]

\[ \text{Total volume of new solution} = 1.2 \, \text{liters} + 2.8 \, \text{liters} = 4 \, \text{liters} \]

### Step 5: Calculate the percentage of sugar in the new solution.
Now we can find the percentage of sugar in the new solution using the formula:

\[ \text{Percentage of sugar} = \left(\frac{\text{Amount of sugar}}{\text{Total volume of new solution}}\right) \times 100 \]

\[ \text{Percentage of sugar} = \left(\frac{1.2 \, \text{liters}}{4 \, \text{liters}}\right) \times 100 = 0.3 \times 100 = 30\% \]

### Final Answer:
The percentage of sugar in the new solution is **30%**.

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