600 g of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution?

Options

A. 160 g
B. 120 g
C. 130g
D. 140 g

Answer

To solve the problem of how much sugar should be added to a 600 g sugar solution that has 40% sugar in order to make it 50% sugar, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the amount of sugar in the original solution**:
- The original solution is 600 g with 40% sugar.
- Amount of sugar = 40% of 600 g = (40/100) * 600 = 240 g.

2. **Let the amount of sugar to be added be X grams**:
- After adding X grams of sugar, the total amount of sugar in the solution will be (240 + X) grams.

3. **Calculate the new total weight of the solution**:
- The new total weight of the solution will be the original weight plus the added sugar:
- Total weight = 600 g + X g = (600 + X) g.

4. **Set up the equation for the new concentration**:
- We want the new solution to have 50% sugar.
- Therefore, we can set up the equation:
\[ \frac{240 + X}{600 + X} = 0.5 \]

5. **Solve the equation**:
- Cross-multiply to eliminate the fraction:
\[ 240 + X = 0.5(600 + X) \]
- Expanding the right side:
\[ 240 + X = 300 + 0.5X \]
- Rearranging the equation:
\[ X - 0.5X = 300 - 240 \]
\[ 0.5X = 60 \]
- Now, divide both sides by 0.5:
\[ X = \frac{60}{0.5} = 120 \text{ grams} \]

6. **Conclusion**:
- Therefore, you need to add **120 grams** of sugar to the solution to make it 50% sugar.