Ratio of milk to water in mixture -A and mixture -b is `3:2` and `5:4` respectively .Mixture -A & mixture -b are mixed to form mixture - C . If quantity of milk is 95 liters more than qunatity of water in mixture - C and ratio of total quantity of mixture -A to that of mixture -B is 14: 9 , then find total quantity of water in mixture -C.

Options

A. A)210 litre
B. B)230 litre
C. C)220 litre
D. D)240 litre

Answer

To solve the problem step by step, we will follow the information given in the question and derive the quantities of milk and water in the mixtures.

### Step 1: Understand the Ratios
The ratio of milk to water in:
- Mixture A is 3:2
- Mixture B is 5:4

This means:
- For every 5 parts of mixture A, 3 parts are milk and 2 parts are water.
- For every 9 parts of mixture B, 5 parts are milk and 4 parts are water.

### Step 2: Set Up the Total Quantities
Let the total quantity of mixture A be \( 14x \) and the total quantity of mixture B be \( 9x \) (based on the ratio of 14:9).

### Step 3: Calculate Milk and Water in Mixture A
In mixture A:
- Total parts = 3 + 2 = 5
- Quantity of milk in A = \( \frac{3}{5} \times 14x = \frac{42x}{5} \)
- Quantity of water in A = \( \frac{2}{5} \times 14x = \frac{28x}{5} \)

### Step 4: Calculate Milk and Water in Mixture B
In mixture B:
- Total parts = 5 + 4 = 9
- Quantity of milk in B = \( \frac{5}{9} \times 9x = 5x \)
- Quantity of water in B = \( \frac{4}{9} \times 9x = 4x \)

### Step 5: Combine Mixtures A and B to Form Mixture C
Now, the total quantities of milk and water in mixture C will be:
- Total milk in C = Milk from A + Milk from B
\[ \text{Milk in C} = \frac{42x}{5} + 5x = \frac{42x}{5} + \frac{25x}{5} = \frac{67x}{5} \]
- Total water in C = Water from A + Water from B
\[ \text{Water in C} = \frac{28x}{5} + 4x = \frac{28x}{5} + \frac{20x}{5} = \frac{48x}{5} \]

### Step 6: Set Up the Equation Based on Given Condition
According to the problem, the quantity of milk in mixture C is 95 liters more than the quantity of water in mixture C:
\[ \frac{67x}{5} = \frac{48x}{5} + 95 \]

### Step 7: Solve for x
To eliminate the fractions, multiply the entire equation by 5:
\[ 67x = 48x + 475 \]
Subtract \( 48x \) from both sides:
\[ 19x = 475 \]
Now, divide by 19:
\[ x = 25 \]

### Step 8: Calculate Total Quantity of Water in Mixture C
Now substitute \( x \) back to find the total quantity of water in mixture C:
\[ \text{Water in C} = \frac{48x}{5} = \frac{48 \times 25}{5} = \frac{1200}{5} = 240 \text{ liters} \]

### Final Answer
The total quantity of water in mixture C is **240 liters**.

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