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 step by step, we need to determine how much sugar should be added to a 600 g sugar solution that currently contains 40% sugar in order to increase the sugar concentration to 50%.

### Step 1: Calculate the amount of sugar in the current solution.
The current solution is 600 g with 40% sugar.

\[ \text{Amount of sugar} = \frac{40}{100} \times 600 = 240 \text{ g} \]

### Step 2: Let \( x \) be the amount of sugar to be added.
We need to find \( x \) such that the new concentration of sugar in the solution becomes 50%.

### Step 3: Set up the equation for the new concentration.
After adding \( x \) grams of sugar, the total amount of sugar will be \( 240 + x \) grams, and the total weight of the solution will be \( 600 + x \) grams. We want this to equal 50% of the new solution.

\[ \frac{240 + x}{600 + x} = \frac{50}{100} \]

### Step 4: Cross-multiply to eliminate the fraction.
Cross-multiplying gives us:

\[ 100(240 + x) = 50(600 + x) \]

### Step 5: Simplify the equation.
Expanding both sides:

\[ 24000 + 100x = 30000 + 50x \]

### Step 6: Rearrange the equation to isolate \( x \).
Subtract \( 50x \) from both sides:

\[ 24000 + 100x - 50x = 30000 \]

This simplifies to:

\[ 24000 + 50x = 30000 \]

Now, subtract 24000 from both sides:

\[ 50x = 30000 - 24000 \]

\[ 50x = 6000 \]

### Step 7: Solve for \( x \).
Dividing both sides by 50 gives:

\[ x = \frac{6000}{50} = 120 \text{ g} \]

### Conclusion:
Therefore, the amount of sugar that should be added to make the solution 50% sugar is **120 g**.

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