If 50% of a certain number is equal to `(3)/(4)`th of another number . What is the ratio between the numbers ?

Options

A. `3:2`
B. `2:5`
C. `5:2`
D. `3:4`

Explanation

To find the ratio between the two numbers based on the given condition, we can follow these steps:

### Step 1: Define the Variables
Let the first number be \( x \) and the second number be \( y \).

### Step 2: Set Up the Equation
According to the problem, 50% of the first number \( x \) is equal to \( \frac{3}{4} \) of the second number \( y \). We can express this mathematically as:
\[ 0.5x = \frac{3}{4}y \]

### Step 3: Convert 50% to a Fraction
50% can be written as \( \frac{50}{100} \) or simplified to \( \frac{1}{2} \). Thus, we can rewrite the equation:
\[ \frac{1}{2}x = \frac{3}{4}y \]

### Step 4: Eliminate the Fraction
To eliminate the fraction, we can multiply both sides of the equation by 4 (the least common multiple of the denominators):
\[ 4 \cdot \frac{1}{2}x = 4 \cdot \frac{3}{4}y \]
This simplifies to:
\[ 2x = 3y \]

### Step 5: Rearrange the Equation
Now, we can rearrange the equation to express \( x \) in terms of \( y \):
\[ x = \frac{3}{2}y \]

### Step 6: Find the Ratio
To find the ratio \( \frac{x}{y} \), we can substitute \( x \) from the previous step:
\[ \frac{x}{y} = \frac{\frac{3}{2}y}{y} \]
This simplifies to:
\[ \frac{x}{y} = \frac{3}{2} \]

### Step 7: Express the Ratio
The ratio of \( x \) to \( y \) can be expressed as:
\[ x : y = 3 : 2 \]

### Final Answer
Thus, the ratio between the two numbers is \( 3 : 2 \).

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