The difference between 71% of a number and 33% of the same number is 24852. What is 56% of that number ?

Options

A. 37425
B. 36624
C. 36812
D. 37224

Answer

To solve the problem step by step, let's denote the unknown number as \( x \).

### Step 1: Set Up the Equation
We know from the problem that the difference between 71% of \( x \) and 33% of \( x \) is 24852. We can express this mathematically as:
\[ 71\% \text{ of } x - 33\% \text{ of } x = 24852 \]
This can be rewritten using decimal form:
\[ 0.71x - 0.33x = 24852 \]

### Step 2: Simplify the Equation
Now, we can simplify the left side of the equation:
\[ (0.71 - 0.33)x = 24852 \]
Calculating \( 0.71 - 0.33 \):
\[ 0.38x = 24852 \]

### Step 3: Solve for \( x \)
To find \( x \), we will divide both sides of the equation by 0.38:
\[ x = \frac{24852}{0.38} \]
Calculating the right side:
\[ x = 65400 \]

### Step 4: Calculate 56% of \( x \)
Now that we have \( x \), we need to find 56% of \( x \):
\[ 56\% \text{ of } x = 0.56 \times x = 0.56 \times 65400 \]
Calculating this:
\[ 0.56 \times 65400 = 36624 \]

### Final Answer
Thus, 56% of the number is:
\[ \boxed{36624} \]