A earns `12(1)/(2)%`  more than B. If they jointly earn Rs. Rs. 35,700 in a year, then the amount that A earns annually is 

Options

A. Rs. 16,800
B. Rs. 17,875
C. Rs. 18,225
D. Rs. 18,900

Answer

To solve the problem step by step, let's denote the earnings of B as \( X \).

### Step 1: Define the earnings of A
Since A earns \( 12.5\% \) more than B, we can express A's earnings as:
\[ A = B + 12.5\% \text{ of } B \]
This can be rewritten as:
\[ A = B + \frac{12.5}{100} \times B = B \left(1 + \frac{12.5}{100}\right) = B \left(\frac{112.5}{100}\right) = 1.125B \]

### Step 2: Set up the equation for total earnings
According to the problem, the total earnings of A and B together is Rs. 35,700. Therefore, we can write:
\[ A + B = 35,700 \]
Substituting the expression for A from Step 1:
\[ 1.125B + B = 35,700 \]

### Step 3: Combine like terms
Combining the terms on the left side gives:
\[ 2.125B = 35,700 \]

### Step 4: Solve for B
To find B, we divide both sides of the equation by 2.125:
\[ B = \frac{35,700}{2.125} \]
Calculating this gives:
\[ B = 16,800 \]

### Step 5: Calculate A's earnings
Now that we have B's earnings, we can find A's earnings using the expression we derived earlier:
\[ A = 1.125B = 1.125 \times 16,800 \]
Calculating this gives:
\[ A = 18,900 \]

### Conclusion
Thus, the amount that A earns annually is Rs. 18,900.

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