If ` 50%` of (p - q) = `30% ` of (p + q) then p : q is equal to

Options

A. ` 5 : 3 `
B. ` 4 : 1 `
C. ` 3 : 5`
D. ` 1 : 4`

Answer

To solve the equation \( 50\% \) of \( (p - q) = 30\% \) of \( (p + q) \), we can follow these steps:

### Step 1: Convert percentages to fractions
We can express \( 50\% \) and \( 30\% \) as fractions:
\[ 50\% = \frac{50}{100} = \frac{1}{2} \]
\[ 30\% = \frac{30}{100} = \frac{3}{10} \]

### Step 2: Write the equation
Using the fractions, we can rewrite the equation:
\[ \frac{1}{2}(p - q) = \frac{3}{10}(p + q) \]

### Step 3: Eliminate the fractions
To eliminate the fractions, we can multiply both sides of the equation by \( 10 \):
\[ 10 \cdot \frac{1}{2}(p - q) = 10 \cdot \frac{3}{10}(p + q) \]
This simplifies to:
\[ 5(p - q) = 3(p + q) \]

### Step 4: Expand both sides
Now, we expand both sides of the equation:
\[ 5p - 5q = 3p + 3q \]

### Step 5: Rearrange the equation
Next, we rearrange the equation to group \( p \) and \( q \):
\[ 5p - 3p = 3q + 5q \]
This simplifies to:
\[ 2p = 8q \]

### Step 6: Solve for the ratio \( p:q \)
Now, we can express \( p \) in terms of \( q \):
\[ p = 4q \]
Thus, the ratio \( p:q \) can be expressed as:
\[ p:q = 4:1 \]

### Final Answer
The ratio \( p:q \) is equal to \( 4:1 \).

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