If 5.5 of a= 0.65 of b, then a : b is equal to—

Options

A. `110:13`
B. `13:11`
C. `11:13`
D. `13:110`

Answer

To solve the problem where \( 5.5a = 0.65b \) and we need to find the ratio \( a : b \), we can follow these steps:

### Step 1: Set up the equation
We start with the equation given in the problem:
\[ 5.5a = 0.65b \]

### Step 2: Rearrange the equation
To find the ratio \( a : b \), we can rearrange the equation to express \( a \) in terms of \( b \):
\[ a = \frac{0.65}{5.5}b \]

### Step 3: Simplify the fraction
Next, we simplify the fraction \( \frac{0.65}{5.5} \):
\[ \frac{0.65}{5.5} = \frac{65}{550} \quad \text{(by multiplying numerator and denominator by 100)} \]
Now we can simplify \( \frac{65}{550} \):
\[ \frac{65 \div 5}{550 \div 5} = \frac{13}{110} \]

### Step 4: Write the ratio
Now that we have \( a \) in terms of \( b \), we can express the ratio \( a : b \):
\[ a : b = \frac{13}{110} : 1 \]
This can be rewritten as:
\[ a : b = 13 : 110 \]

### Step 5: Final answer
Thus, the ratio \( a : b \) is:
\[ \boxed{13 : 110} \]