A 600 grams of sugar solution contains 50% sugar. How much sugar (in grams) must be added so that the new mixture contains 60% sugar?

Options

A. 120
B. 150
C. 175
D. 200

Answer

To solve the problem, we need to determine how much sugar must be added to a 600-gram sugar solution that currently contains 50% sugar, in order to achieve a new mixture that contains 60% sugar.

### Step-by-Step Solution:

1. **Calculate the amount of sugar in the initial solution:**
- The initial solution weighs 600 grams and contains 50% sugar.
- Amount of sugar = 50% of 600 grams
\[ \text{Amount of sugar} = \frac{50}{100} \times 600 = 300 \text{ grams} \]

2. **Determine the amount of water in the initial solution:**
- Since the solution is 50% sugar, the remaining 50% is water.
- Amount of water = 600 grams - 300 grams of sugar
\[ \text{Amount of water} = 600 - 300 = 300 \text{ grams} \]

3. **Let \( x \) be the amount of sugar to be added:**
- After adding \( x \) grams of sugar, the total amount of sugar in the solution will be \( 300 + x \) grams.
- The total weight of the new solution will be \( 600 + x \) grams.

4. **Set up the equation for the new percentage of sugar:**
- We want the new solution to contain 60% sugar.
- Therefore, we can set up the equation:
\[ \frac{300 + x}{600 + x} = \frac{60}{100} \]

5. **Cross-multiply to solve for \( x \):**
\[ 100(300 + x) = 60(600 + x) \]
\[ 30000 + 100x = 36000 + 60x \]

6. **Rearrange the equation:**
\[ 100x - 60x = 36000 - 30000 \]
\[ 40x = 6000 \]

7. **Solve for \( x \):**
\[ x = \frac{6000}{40} = 150 \text{ grams} \]

### Final Answer:
To achieve a new mixture that contains 60% sugar, **150 grams of sugar must be added.**

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