If 60% of (x - y) = 45% (x + y) and y=k% of x, then 49% of k is equal to:

Options

A. 7
B. 5
C. 9
D. 6

Answer

To solve the problem step by step, we start with the given equation and the relationship between \( y \) and \( x \).

### Step 1: Set up the equation
We are given:
\[ 60\% \text{ of } (x - y) = 45\% \text{ of } (x + y) \]
This can be rewritten as:
\[ 0.6(x - y) = 0.45(x + y) \]

### Step 2: Remove the percentages
To eliminate the decimals, we can multiply both sides by 100:
\[ 60(x - y) = 45(x + y) \]

### Step 3: Expand both sides
Expanding both sides gives:
\[ 60x - 60y = 45x + 45y \]

### Step 4: Rearrange the equation
Now, we will rearrange the equation to isolate \( x \) and \( y \):
\[ 60x - 45x = 60y + 45y \]
This simplifies to:
\[ 15x = 105y \]

### Step 5: Simplify the equation
Dividing both sides by 15 gives:
\[ x = 7y \]

### Step 6: Substitute \( y \) in terms of \( x \)
We know from the problem statement that \( y = k\% \text{ of } x \):
\[ y = \frac{k}{100} x \]

### Step 7: Substitute \( y \) in the equation
Substituting \( y \) into the equation \( x = 7y \):
\[ x = 7\left(\frac{k}{100} x\right) \]

### Step 8: Solve for \( k \)
Now, we can simplify this:
\[ x = \frac{7k}{100} x \]
Assuming \( x \neq 0 \), we can divide both sides by \( x \):
\[ 1 = \frac{7k}{100} \]
Multiplying both sides by 100 gives:
\[ 100 = 7k \]
Thus,
\[ k = \frac{100}{7} \]

### Step 9: Calculate \( 49\% \text{ of } k \)
Now we need to find \( 49\% \text{ of } k \):
\[ 49\% \text{ of } k = 0.49k = 0.49 \times \frac{100}{7} \]
Calculating this gives:
\[ = \frac{49 \times 100}{7 \times 100} = \frac{4900}{700} = 7 \]

### Final Answer
Thus, \( 49\% \text{ of } k \) is equal to:
\[ \boxed{7} \]