If 0.8 x A = 0.09 x B, then find A : B.

Options

A. `9 : 80`
B. `3 : 80`
C. `80 : 9`
D. `7 : 80`

Answer

To solve the equation \( 0.8 \times A = 0.09 \times B \) and find the ratio \( A : B \), follow these steps:

### Step 1: Write the equation
We start with the equation given in the problem:
\[ 0.8 \times A = 0.09 \times B \]

### Step 2: Rearrange the equation
To express \( A \) in terms of \( B \), we can rearrange the equation. We can do this by dividing both sides by \( 0.8 \):
\[ A = \frac{0.09 \times B}{0.8} \]

### Step 3: Simplify the expression
Now, we simplify the right-hand side:
\[ A = \frac{0.09}{0.8} \times B \]

### Step 4: Calculate \( \frac{0.09}{0.8} \)
To simplify \( \frac{0.09}{0.8} \), we can convert both numbers into fractions:
\[ \frac{0.09}{0.8} = \frac{9}{100} \div \frac{8}{10} = \frac{9}{100} \times \frac{10}{8} = \frac{9 \times 10}{100 \times 8} = \frac{90}{800} = \frac{9}{80} \]
Thus, we have:
\[ A = \frac{9}{80} \times B \]

### Step 5: Express the ratio \( A : B \)
Now we can express the ratio \( A : B \):
\[ A : B = \frac{9}{80} : 1 \]
This can be rewritten as:
\[ A : B = 9 : 80 \]

### Final Answer
The ratio \( A : B \) is:
\[ \boxed{9 : 80} \]

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