A jar contains a mixture of two liquids A and B in the ratio `3:1`. When 24 litres of the mixture is taken out and 9 litres of liquid B is poured into the jar, the ratio becomes `3 :4`. How many litres of liquid A was contained in the jar?

Options

A. 30 ltr
B. 27 ltr
C. 21 ltr
D. 24 ltr

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the initial ratio of liquids A and B
The initial ratio of liquid A to liquid B is given as 3:1. This means if we let the quantity of liquid A be \(3x\), then the quantity of liquid B will be \(x\).

### Step 2: Calculate the total initial volume of the mixture
The total volume of the mixture can be expressed as:
\[ \text{Total volume} = 3x + x = 4x \]

### Step 3: Determine the amount of liquid A and B in the 24 liters taken out
When 24 liters of the mixture is taken out, the amount of liquid A taken out can be calculated using the ratio:
\[ \text{Liquid A taken out} = \frac{3x}{4x} \times 24 = \frac{3}{4} \times 24 = 18 \text{ liters} \]
Similarly, the amount of liquid B taken out is:
\[ \text{Liquid B taken out} = \frac{x}{4x} \times 24 = \frac{1}{4} \times 24 = 6 \text{ liters} \]

### Step 4: Calculate the remaining amounts of liquids A and B
After taking out 24 liters:
- Remaining liquid A:
\[ \text{Remaining A} = 3x - 18 \]
- Remaining liquid B:
\[ \text{Remaining B} = x - 6 \]

### Step 5: Add 9 liters of liquid B to the jar
After adding 9 liters of liquid B, the new amount of liquid B becomes:
\[ \text{New B} = (x - 6) + 9 = x + 3 \]

### Step 6: Set up the new ratio of liquids A and B
The new ratio of liquid A to liquid B is given as 3:4. Therefore, we can set up the equation:
\[ \frac{3x - 18}{x + 3} = \frac{3}{4} \]

### Step 7: Cross-multiply to solve for x
Cross-multiplying gives:
\[ 4(3x - 18) = 3(x + 3) \]
Expanding both sides:
\[ 12x - 72 = 3x + 9 \]

### Step 8: Rearranging the equation
Now, we will rearrange the equation to isolate \(x\):
\[ 12x - 3x = 9 + 72 \]
\[ 9x = 81 \]
\[ x = 9 \]

### Step 9: Calculate the quantity of liquid A
Since the quantity of liquid A is \(3x\):
\[ \text{Liquid A} = 3 \times 9 = 27 \text{ liters} \]

### Final Answer
The quantity of liquid A contained in the jar is **27 liters**.

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