In a mixture, ink and water are in the ratio of `8 : 5`. If 24 litres of water is added to the mixture, then the new ratio becomes `8:11`. What is the total quantity (in litres) of water in the new mixture ?

Options

A. 40
B. 42
C. 44
D. 48

Answer

To solve the problem step by step, we will first establish the initial quantities of ink and water based on the given ratio, then incorporate the addition of water, and finally calculate the total quantity of water in the new mixture.

### Step 1: Establish the initial quantities of ink and water
Given the ratio of ink to water is 8:5, we can represent the quantities of ink and water as:
- Ink = 8x
- Water = 5x

### Step 2: Determine the new ratio after adding water
When 24 liters of water is added, the new quantity of water becomes:
- New Water = 5x + 24

The new ratio of ink to water is given as 8:11. Therefore, we can set up the equation:
\[ \frac{8x}{5x + 24} = \frac{8}{11} \]

### Step 3: Cross-multiply to solve for x
Cross-multiplying gives us:
\[ 8 \cdot (5x + 24) = 11 \cdot 8x \]
Expanding both sides:
\[ 40x + 192 = 88x \]

### Step 4: Rearranging the equation
Rearranging the equation to isolate x:
\[ 192 = 88x - 40x \]
\[ 192 = 48x \]
\[ x = \frac{192}{48} = 4 \]

### Step 5: Calculate the initial quantities of ink and water
Now that we have x, we can find the initial quantities:
- Ink = 8x = 8 * 4 = 32 liters
- Water = 5x = 5 * 4 = 20 liters

### Step 6: Calculate the new quantity of water
After adding 24 liters of water, the new quantity of water becomes:
\[ \text{New Water} = 20 + 24 = 44 \text{ liters} \]

### Final Answer
The total quantity of water in the new mixture is **44 liters**.

---