The milk and water in a mixture are in the ratio 7:5. When 15 litres of water are added to it, the ratio of milk and water in the new mixture becomes 7:8. The total quantity of water in the new mixture is

Options

A. 35litres
B. 40litres
C. 60litres
D. 96litres

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the initial ratio of milk and water
The initial ratio of milk to water is given as 7:5. This means for every 7 parts of milk, there are 5 parts of water.

### Step 2: Define the quantities of milk and water
Let the quantity of milk be \( 7x \) liters and the quantity of water be \( 5x \) liters, where \( x \) is a common multiplier.

### Step 3: Add water to the mixture
We are told that 15 liters of water are added to the mixture. Therefore, the new quantity of water becomes:
\[ \text{New quantity of water} = 5x + 15 \]

### Step 4: Set up the new ratio
After adding the water, the new ratio of milk to water becomes 7:8. Therefore, we can set up the equation:
\[ \frac{7x}{5x + 15} = \frac{7}{8} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 7x \cdot 8 = 7 \cdot (5x + 15) \]
This simplifies to:
\[ 56x = 35x + 105 \]

### Step 6: Solve for \( x \)
Subtract \( 35x \) from both sides:
\[ 56x - 35x = 105 \]
\[ 21x = 105 \]
Now, divide by 21:
\[ x = 5 \]

### Step 7: Calculate the original quantities of milk and water
Now that we have \( x \), we can find the original quantities:
- Milk = \( 7x = 7 \times 5 = 35 \) liters
- Water = \( 5x = 5 \times 5 = 25 \) liters

### Step 8: Calculate the total quantity of water in the new mixture
After adding 15 liters of water, the total quantity of water becomes:
\[ \text{Total water} = 25 + 15 = 40 \text{ liters} \]

### Final Answer
The total quantity of water in the new mixture is **40 liters**.

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