There is `50%` alcohol in the 9ml saving lotion. How much water should be mixed in it so that new mixture has `30%` alcohol ?

Options

A. `6` ltr
B. `8` ltr
C. `5` ltr
D. `7` ltr

Answer

To solve the problem step by step, we need to determine how much water should be mixed with the 9 ml saving lotion that contains 50% alcohol to achieve a new mixture that has 30% alcohol.

### Step 1: Calculate the amount of alcohol in the original lotion.
The original lotion is 9 ml with 50% alcohol.

\[ \text{Amount of alcohol} = \text{Total volume} \times \text{Percentage of alcohol} \]
\[ \text{Amount of alcohol} = 9 \, \text{ml} \times 0.50 = 4.5 \, \text{ml} \]

### Step 2: Let the amount of water to be added be \( x \) ml.
After adding \( x \) ml of water, the total volume of the mixture will be \( 9 + x \) ml.

### Step 3: Set up the equation for the new concentration of alcohol.
We want the new mixture to have 30% alcohol. Therefore, we can set up the equation:

\[ \frac{\text{Amount of alcohol}}{\text{Total volume of mixture}} = \text{Percentage of alcohol in new mixture} \]
\[ \frac{4.5}{9 + x} = 0.30 \]

### Step 4: Solve for \( x \).
Cross-multiply to solve for \( x \):

\[ 4.5 = 0.30 \times (9 + x) \]
\[ 4.5 = 2.7 + 0.30x \]
\[ 4.5 - 2.7 = 0.30x \]
\[ 1.8 = 0.30x \]
\[ x = \frac{1.8}{0.30} = 6 \, \text{ml} \]

### Conclusion:
The amount of water that should be mixed in the lotion to achieve a 30% alcohol concentration is **6 ml**.

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