In a mixture of 45 litres, the ratio of liquid A and liquid B is 7 : 2. If 11 litres of liquid B is added to the mixture, then what will be the ratio of liquid A and liquid B in the new mixture?

Options

A. `7:4`
B. `8:5`
C. `6:5`
D. `5:3`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the initial mixture
We have a mixture of 45 liters with a ratio of liquid A to liquid B as 7:2.

### Step 2: Calculate the total parts in the ratio
The total parts in the ratio of liquid A to liquid B is:
\[ 7 + 2 = 9 \text{ parts} \]

### Step 3: Calculate the volume of liquid A and liquid B
To find the volume of each liquid, we can use the total volume of the mixture (45 liters) and divide it according to the ratio.

- Volume of liquid A:
\[ \text{Volume of A} = \left(\frac{7}{9}\right) \times 45 = 35 \text{ liters} \]

- Volume of liquid B:
\[ \text{Volume of B} = \left(\frac{2}{9}\right) \times 45 = 10 \text{ liters} \]

### Step 4: Add 11 liters of liquid B to the mixture
Now, we add 11 liters of liquid B to the existing 10 liters of liquid B.

- New volume of liquid B:
\[ \text{New Volume of B} = 10 + 11 = 21 \text{ liters} \]

### Step 5: Determine the new ratio of liquid A to liquid B
Now we have:
- Volume of liquid A = 35 liters
- Volume of liquid B = 21 liters

The new ratio of liquid A to liquid B is:
\[ \text{Ratio of A to B} = \frac{35}{21} \]

### Step 6: Simplify the ratio
To simplify the ratio:
\[ \frac{35}{21} = \frac{5}{3} \]

Thus, the ratio of liquid A to liquid B in the new mixture is 5:3.

### Final Answer
The new ratio of liquid A to liquid B is **5:3**.

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