In a mixture, sugar and milk are in the ratio 4 : 5. If 7 litres of milk is added to it, then the ratio of sugar and milk in the new mixture becomes 2 : 3. What is the total quantity (In litres) of sugar in new mixture?

Options

A. 35
B. 28
C. 42
D. 24

Explanation

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

### Step 1: Understand the initial ratio
The initial ratio of sugar to milk is given as 4:5. This means that for every 4 parts of sugar, there are 5 parts of milk.

### Step 2: Define the quantities
Let the quantity of sugar be \( 4x \) liters and the quantity of milk be \( 5x \) liters, where \( x \) is a common multiplier.

### Step 3: Add the milk
According to the problem, 7 liters of milk is added to the mixture. Therefore, the new quantity of milk becomes:
\[ \text{New quantity of milk} = 5x + 7 \]

### Step 4: Set up the new ratio
After adding the milk, the new ratio of sugar to milk is given as 2:3. This can be expressed as:
\[ \frac{4x}{5x + 7} = \frac{2}{3} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 4x \cdot 3 = 2 \cdot (5x + 7) \]
This simplifies to:
\[ 12x = 10x + 14 \]

### Step 6: Solve for \( x \)
Now, we can isolate \( x \):
\[ 12x - 10x = 14 \\ 2x = 14 \\ x = 7 \]

### Step 7: Calculate the quantity of sugar
Now that we have \( x \), we can find the quantity of sugar:
\[ \text{Quantity of sugar} = 4x = 4 \cdot 7 = 28 \text{ liters} \]

### Step 8: Conclusion
The total quantity of sugar in the new mixture is **28 liters**.

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