A jar contains x litres of mixture of liquids- A and B, in the respective ratio of `2:3`. Six liters each of the liquids- A and B, was added to the mixture in the jar, as a result of which the quantity of liquid A was 18 litres less than that of liquid B. What is the value of x ?

Options

A. 100
B. 75
C. 90
D. 80

Answer

To solve the problem, we need to find the value of \( x \) given the conditions about the liquids A and B in the jar.

### Step 1: Define the initial quantities of liquids A and B
Let the initial quantities of liquids A and B in the jar be represented as follows:
- Let the quantity of liquid A be \( 2k \) liters.
- Let the quantity of liquid B be \( 3k \) liters.

Since the ratio of A to B is \( 2:3 \), we can express the total volume \( x \) as:
\[ x = 2k + 3k = 5k \]

### Step 2: Add the additional quantities of liquids A and B
We are told that 6 liters of liquid A and 6 liters of liquid B are added to the mixture. Therefore, the new quantities of liquids A and B become:
- New quantity of liquid A = \( 2k + 6 \) liters
- New quantity of liquid B = \( 3k + 6 \) liters

### Step 3: Set up the equation based on the given condition
According to the problem, after adding the liquids, the quantity of liquid A is 18 liters less than that of liquid B. This gives us the equation:
\[ 2k + 6 = (3k + 6) - 18 \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ 2k + 6 = 3k + 6 - 18 \]
\[ 2k + 6 = 3k - 12 \]

### Step 5: Rearrange the equation to isolate \( k \)
Rearranging the equation gives:
\[ 2k + 6 + 12 = 3k \]
\[ 18 = 3k - 2k \]
\[ 18 = k \]

### Step 6: Calculate the value of \( x \)
Now that we have \( k \), we can find \( x \):
\[ x = 5k = 5 \times 18 = 90 \]

### Conclusion
Thus, the value of \( x \) is \( \boxed{90} \) liters.

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