The ratio of incomes of A and B is `5 : 6`. If A gets rs 1,100 less than B, their total income (in rupees) is

Options

A. 9900
B. 12100
C. 14400
D. 10000

Answer

To solve the problem step by step, we will follow these instructions:

1. **Understand the Ratio**: The ratio of incomes of A and B is given as 5:6. This means if A's income is 5 parts, B's income is 6 parts.

2. **Express Incomes in Terms of a Variable**: Let the income of A be \(5x\) and the income of B be \(6x\), where \(x\) is a common multiplier.

3. **Set Up the Equation Based on the Given Information**: According to the problem, A gets Rs 1,100 less than B. Therefore, we can write the equation:
\[ 6x - 5x = 1100 \]

4. **Solve for \(x\)**: Simplifying the equation gives:
\[ x = 1100 \]

5. **Calculate Incomes of A and B**: Now that we have the value of \(x\), we can find the actual incomes:
- A's income:
\[ 5x = 5 \times 1100 = 5500 \]
- B's income:
\[ 6x = 6 \times 1100 = 6600 \]

6. **Calculate Total Income**: The total income of A and B is:
\[ 5500 + 6600 = 12100 \]

Thus, the total income of A and B is Rs 12,100.