Two solutions of 90% and 97% purity are mixed resulting in 21 litres of mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture?

Options

A. 15 litres
B. 12 litres
C. 9 litres
D. 6 litres

Answer

To solve the problem step by step, we will use the concept of alligation. Here’s how we can find the quantity of the first solution in the resulting mixture:

### Step 1: Define the Purities
Let:
- Solution A (first solution) has a purity of 90%.
- Solution B (second solution) has a purity of 97%.
- The resulting mixture has a purity of 94%.

### Step 2: Set Up the Alligation
We will use the alligation method to find the ratio in which the two solutions are mixed.

1. Calculate the difference between the purity of Solution A and the purity of the mixture:
\[ 94\% - 90\% = 4\% \]

2. Calculate the difference between the purity of Solution B and the purity of the mixture:
\[ 97\% - 94\% = 3\% \]

### Step 3: Determine the Ratio
The ratio of the two solutions can be determined by the differences calculated:
- The ratio of Solution A to Solution B is:
\[ \text{Ratio} = 3 : 4 \]

### Step 4: Calculate Total Parts
The total parts of the mixture can be calculated by adding the parts of both solutions:
\[ 3 + 4 = 7 \text{ parts} \]

### Step 5: Calculate the Quantity of Each Solution
The total volume of the mixture is given as 21 liters. We can find the quantity of each solution using the ratio.

1. Quantity of Solution A (90% purity):
\[ \text{Quantity of Solution A} = \frac{3}{7} \times 21 = 9 \text{ liters} \]

2. Quantity of Solution B (97% purity):
\[ \text{Quantity of Solution B} = \frac{4}{7} \times 21 = 12 \text{ liters} \]

### Step 6: Conclusion
The quantity of the first solution (90% purity) in the resulting mixture is:
\[ \boxed{9 \text{ liters}} \]

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