If `60%` of K is 30 less than `75%` of K, then what is the value of K ?

Options

A. 500
B. 300
C. 400
D. 200

Explanation

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the problem
We need to translate the statement "60% of K is 30 less than 75% of K" into a mathematical equation.

### Step 2: Write the equation
We can express the percentages as fractions:
- 60% of K can be written as \( \frac{60}{100}K \) or \( 0.6K \).
- 75% of K can be written as \( \frac{75}{100}K \) or \( 0.75K \).

According to the problem, we can set up the equation:
\[ 0.6K = 0.75K - 30 \]

### Step 3: Rearrange the equation
To isolate K, we need to move all terms involving K to one side of the equation. We can do this by subtracting \( 0.6K \) from both sides:
\[ 0.6K - 0.6K = 0.75K - 0.6K - 30 \]
This simplifies to:
\[ 0 = 0.15K - 30 \]

### Step 4: Solve for K
Now we can add 30 to both sides:
\[ 30 = 0.15K \]

Next, we divide both sides by \( 0.15 \) to solve for K:
\[ K = \frac{30}{0.15} \]

### Step 5: Calculate the value of K
To calculate \( \frac{30}{0.15} \):
\[ K = 30 \div 0.15 = 200 \]

### Final Answer
Thus, the value of K is \( 200 \).

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