The income of A is `40%` more than B's income. B's income is `20%` less than C's income. Find the ratio of income of A and C.

Answer

To find the ratio of the income of A and C, we will follow these steps:

### Step 1: Define the incomes
Let B's income be represented as \( B \). According to the problem, A's income is 40% more than B's income.

### Step 2: Calculate A's income in terms of B
A's income can be calculated as follows:
\[ A = B + 0.4B = 1.4B \]

### Step 3: Express C's income in terms of B
We know that B's income is 20% less than C's income. Therefore, we can express C's income as:
\[ B = C - 0.2C = 0.8C \]
From this, we can express C in terms of B:
\[ C = \frac{B}{0.8} = 1.25B \]

### Step 4: Find the ratio of A's income to C's income
Now we have A's income as \( 1.4B \) and C's income as \( 1.25B \). The ratio of A's income to C's income can be calculated as:
\[ \text{Ratio of A to C} = \frac{A}{C} = \frac{1.4B}{1.25B} \]
The \( B \) cancels out:
\[ \text{Ratio of A to C} = \frac{1.4}{1.25} \]

### Step 5: Simplify the ratio
To simplify \( \frac{1.4}{1.25} \), we can convert both numbers to fractions:
\[ 1.4 = \frac{14}{10} = \frac{7}{5} \]
\[ 1.25 = \frac{5}{4} \]
Now, substituting these fractions into the ratio gives:
\[ \frac{A}{C} = \frac{\frac{7}{5}}{\frac{5}{4}} = \frac{7}{5} \times \frac{4}{5} = \frac{28}{25} \]

### Final Answer
Thus, the ratio of the income of A to C is:
\[ \text{Ratio of A to C} = 28:25 \]

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