If 35% of A's income is equal to 25% of B's income, then the ra tio of A's income to B's income is

Options

A. A) `7:5`
B. B) `5:7`
C. C) `4:7`
D. D) `4:3`

Answer

To find the ratio of A's income to B's income given that 35% of A's income is equal to 25% of B's income, we can follow these steps:

### Step 1: Set up the equation
Let A's income be represented as \( A \) and B's income as \( B \). According to the problem, we have:
\[ 0.35A = 0.25B \]

### Step 2: Rearrange the equation
To find the ratio of A's income to B's income, we can rearrange the equation:
\[ \frac{A}{B} = \frac{0.25}{0.35} \]

### Step 3: Simplify the fraction
Now, we simplify the fraction \( \frac{0.25}{0.35} \):
\[ \frac{0.25}{0.35} = \frac{25}{35} \]

### Step 4: Reduce the fraction
Next, we can reduce \( \frac{25}{35} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
\[ \frac{25 \div 5}{35 \div 5} = \frac{5}{7} \]

### Step 5: Write the final ratio
Thus, the ratio of A's income to B's income is:
\[ A : B = 5 : 7 \]

### Final Answer
The ratio of A's income to B's income is \( 5 : 7 \).

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