Six-eleventh of the first number is equal to 54% of the second number. What is the respective ratio between the first and the second numbers ?

Options

A. 0.38194444444444
B. 99 : 100
C. 0.86111111111111
D. 99 . 101

Answer

To solve the problem step by step, we will define the first number as \( A \) and the second number as \( B \).

### Step 1: Set up the equation
We know from the problem statement that:
\[ \frac{6}{11} A = 54\% \text{ of } B \]
We can express \( 54\% \) as a fraction:
\[ 54\% = \frac{54}{100} = \frac{27}{50} \]
Thus, we can rewrite the equation as:
\[ \frac{6}{11} A = \frac{27}{50} B \]

### Step 2: Cross-multiply to eliminate the fractions
To eliminate the fractions, we will cross-multiply:
\[ 6 \cdot 50 A = 27 \cdot 11 B \]
This simplifies to:
\[ 300 A = 297 B \]

### Step 3: Rearrange the equation to find the ratio
Now, we can rearrange the equation to express the ratio of \( A \) to \( B \):
\[ \frac{A}{B} = \frac{297}{300} \]

### Step 4: Simplify the ratio
To simplify the ratio \( \frac{297}{300} \), we can find the greatest common divisor (GCD) of 297 and 300. The GCD is 3.
So we divide both the numerator and the denominator by 3:
\[ \frac{A}{B} = \frac{99}{100} \]

### Conclusion
The respective ratio between the first number \( A \) and the second number \( B \) is:
\[ \text{Ratio of } A \text{ to } B = 99:100 \]

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