If 60% of (x — y) =45% (x + y) and y = k% ofx, then 21% of k is equal to

Options

A. 7
B. 6
C. 3
D. 1

Answer

To solve the problem step by step, we start with the given equation and information.

### Step 1: Write the given equation
We have the equation:
\[ 60\% \text{ of } (x - y) = 45\% \text{ of } (x + y) \]

### Step 2: Convert percentages to fractions
Convert the percentages to fractions:
\[ \frac{60}{100}(x - y) = \frac{45}{100}(x + y) \]

### Step 3: Simplify the equation
Multiply both sides by 100 to eliminate the fractions:
\[ 60(x - y) = 45(x + y) \]

### Step 4: Expand both sides
Expanding both sides gives:
\[ 60x - 60y = 45x + 45y \]

### Step 5: Rearrange the equation
Rearranging the equation to isolate terms involving \(x\) and \(y\):
\[ 60x - 45x = 60y + 45y \]
\[ 15x = 105y \]

### Step 6: Simplify the equation
Dividing both sides by 15:
\[ x = 7y \]

### Step 7: Substitute \(y\) in terms of \(x\)
From the problem, we know that:
\[ y = k\% \text{ of } x \]
This can be written as:
\[ y = \frac{k}{100}x \]

### Step 8: Equate the two expressions for \(y\)
Now we can equate the two expressions for \(y\):
\[ 7y = x \]
Substituting \(y\) gives:
\[ 7\left(\frac{k}{100}x\right) = x \]

### Step 9: Solve for \(k\)
Dividing both sides by \(x\) (assuming \(x \neq 0\)):
\[ \frac{7k}{100} = 1 \]
Multiplying both sides by 100:
\[ 7k = 100 \]
Dividing by 7:
\[ k = \frac{100}{7} \]

### Step 10: Calculate \(21\%\) of \(k\)
Now we need to find \(21\%\) of \(k\):
\[ 21\% \text{ of } k = \frac{21}{100} \times k = \frac{21}{100} \times \frac{100}{7} \]

### Step 11: Simplify the expression
This simplifies to:
\[ = \frac{21}{7} = 3 \]

### Final Answer
Thus, \(21\%\) of \(k\) is equal to \(3\).