If 35% of A is equal to 60% of B, then what is the ratio of A and B?

Options

A. `8:13 `
B. `12:7`
C. ` 2:3`
D. `13:7 `

Answer

To solve the problem where 35% of A is equal to 60% of B, we can follow these steps:

### Step 1: Set up the equation
We start with the given information:
\[ 35\% \text{ of } A = 60\% \text{ of } B \]

This can be written in equation form as:
\[ 0.35A = 0.60B \]

### Step 2: Rearrange the equation
To find the ratio of A to B, we can rearrange the equation to isolate A and B:
\[ \frac{A}{B} = \frac{0.60}{0.35} \]

### Step 3: Simplify the fraction
Now we simplify the fraction:
\[ \frac{0.60}{0.35} = \frac{60}{35} \]

To simplify \( \frac{60}{35} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 5:
\[ \frac{60 \div 5}{35 \div 5} = \frac{12}{7} \]

### Step 4: Write the final ratio
Thus, the ratio of A to B is:
\[ A : B = 12 : 7 \]

### Final Answer
The ratio of A to B is \( 12 : 7 \).

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