If the income of A is `10%` more than of B and the income of B is `20%` less than that of C, then the incomes of A,B,C are in the ratio.

Options

A. `11 : 10 : 8`
B. `10 : 9 : 7`
C. `22 : 18 : 25`
D. `22 : 20 : 25`

Answer

To solve the problem step by step, we need to establish the relationships between the incomes of A, B, and C based on the given percentages.

### Step-by-Step Solution:

1. **Define the Income of B**:
Let the income of B be represented as \( B = x \).

2. **Calculate the Income of A**:
Since A's income is 10% more than B's, we can express A's income as:
\[ A = B + 10\% \text{ of } B = x + 0.1x = 1.1x \]

3. **Calculate the Income of C**:
B's income is 20% less than C's income. Therefore, we can express C's income as:
\[ B = C - 20\% \text{ of } C = C - 0.2C = 0.8C \]
Rearranging this gives us:
\[ C = \frac{B}{0.8} = \frac{x}{0.8} = 1.25x \]

4. **Establish the Ratios**:
Now we have the incomes of A, B, and C in terms of \( x \):
- \( A = 1.1x \)
- \( B = x \)
- \( C = 1.25x \)

5. **Express the Ratios**:
To find the ratio of A, B, and C, we can express it as:
\[ A : B : C = 1.1x : x : 1.25x \]
Dividing each term by \( x \) simplifies this to:
\[ A : B : C = 1.1 : 1 : 1.25 \]

6. **Convert to Whole Numbers**:
To eliminate the decimals, we can multiply each term by 100 to convert them to whole numbers:
\[ A : B : C = 110 : 100 : 125 \]

7. **Simplify the Ratio**:
Now, we can simplify the ratio:
- The GCD of 110, 100, and 125 is 5.
- Dividing each term by 5 gives:
\[ A : B : C = 22 : 20 : 25 \]

### Final Answer:
The incomes of A, B, and C are in the ratio **22 : 20 : 25**.

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