A sample of 50 L of glycerine is found to be adulterated to the extent of 20%. Find how much pure gly- cerine should be added to bring down percentage of impurity to 5%?

Options

A. 100 L
B. 130 L
C. 140 L
D. 150 L

Answer

To solve the problem of how much pure glycerine should be added to a 50 L sample that is 20% adulterated in order to reduce the impurity percentage to 5%, we can follow these steps:

### Step 1: Determine the amount of impurity in the current sample
The sample is 50 L and is 20% adulterated. Therefore, the amount of impurity can be calculated as:

\[ \text{Amount of Impurity} = \text{Total Volume} \times \text{Percentage of Impurity} \]
\[ \text{Amount of Impurity} = 50 \, \text{L} \times \frac{20}{100} = 10 \, \text{L} \]

### Step 2: Determine the amount of pure glycerine in the current sample
To find the amount of pure glycerine, we subtract the amount of impurity from the total volume:

\[ \text{Amount of Pure Glycerine} = \text{Total Volume} - \text{Amount of Impurity} \]
\[ \text{Amount of Pure Glycerine} = 50 \, \text{L} - 10 \, \text{L} = 40 \, \text{L} \]

### Step 3: Set up the equation for the new scenario
Let \( x \) be the amount of pure glycerine to be added. After adding \( x \) liters of pure glycerine, the new total volume will be:

\[ \text{New Total Volume} = 50 \, \text{L} + x \]

The amount of impurity remains the same (10 L), and we want the new percentage of impurity to be 5%. Therefore, we can set up the equation:

\[ \frac{\text{Amount of Impurity}}{\text{New Total Volume}} = \frac{5}{100} \]
Substituting the known values:

\[ \frac{10}{50 + x} = \frac{5}{100} \]

### Step 4: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:

\[ 10 \times 100 = 5 \times (50 + x) \]
\[ 1000 = 250 + 5x \]

### Step 5: Solve for \( x \)
Rearranging the equation to isolate \( x \):

\[ 1000 - 250 = 5x \]
\[ 750 = 5x \]
\[ x = \frac{750}{5} = 150 \]

### Conclusion
Thus, the amount of pure glycerine that should be added to bring down the percentage of impurity to 5% is **150 L**.

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