In 2004, the total monthly salary of A and B together was Rs 18000.‘In 2005 monthly salary of A and B increased by `14%` and `20%` respectively from previous year. If after the given increment A’s salary became `76%` of B’s salary. What was A’s salary in 2004 (that is before the mentioned increment of 2005) ?

Options

A. Rs 7,500
B. Rs 8,000
C. Rs 6,500
D. Rs 8,500

Answer

To solve the problem step by step, we will follow the given information and perform calculations accordingly.

### Step 1: Define the Salaries
Let the salary of A in 2004 be \( X \) and the salary of B in 2004 be \( Y \). According to the problem, we know:
\[ X + Y = 18000 \]

### Step 2: Calculate the Salaries After Increment
In 2005, A's salary increases by 14% and B's salary increases by 20%. Therefore, the new salaries can be expressed as:
\[ \text{Salary of A in 2005} = X + 0.14X = 1.14X \]
\[ \text{Salary of B in 2005} = Y + 0.20Y = 1.20Y \]

### Step 3: Establish the Relationship Between A's and B's Salaries
According to the problem, after the increment, A's salary becomes 76% of B's salary:
\[ 1.14X = 0.76 \times 1.20Y \]

### Step 4: Simplify the Equation
We can simplify the equation:
\[ 1.14X = 0.912Y \]
Now, rearranging gives us:
\[ \frac{X}{Y} = \frac{0.912}{1.14} \]
Calculating the ratio:
\[ \frac{X}{Y} = \frac{912}{1140} = \frac{76}{95} \]

### Step 5: Express Y in Terms of X
From the ratio \( \frac{X}{Y} = \frac{76}{95} \), we can express \( Y \) in terms of \( X \):
\[ Y = \frac{95}{76}X \]

### Step 6: Substitute into the Total Salary Equation
Now, substituting \( Y \) back into the total salary equation:
\[ X + \frac{95}{76}X = 18000 \]
Combining the terms:
\[ \frac{76X + 95X}{76} = 18000 \]
\[ \frac{171X}{76} = 18000 \]

### Step 7: Solve for X
Now, we can solve for \( X \):
\[ 171X = 18000 \times 76 \]
Calculating \( 18000 \times 76 \):
\[ 171X = 1368000 \]
Now, dividing both sides by 171:
\[ X = \frac{1368000}{171} \approx 8000 \]

### Conclusion
Thus, A's salary in 2004 was:
\[ \boxed{8000} \]