The difference between 38% of a number and 24% of the same number is 135.10. What is 40% of that number?

Options

A. 394
B. 370
C. 378
D. 386

Answer

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

### Step 1: Set up the equation
We know that the difference between 38% of the number and 24% of the same number is 135.10. We can express this mathematically as:
\[ 0.38x - 0.24x = 135.10 \]

### Step 2: Simplify the equation
Now, we can simplify the left-hand side of the equation:
\[ (0.38 - 0.24)x = 135.10 \]
\[ 0.14x = 135.10 \]

### Step 3: Solve for \( x \)
Next, we need to isolate \( x \) by dividing both sides of the equation by 0.14:
\[ x = \frac{135.10}{0.14} \]

### Step 4: Calculate \( x \)
Now, we perform the division:
\[ x = 965 \]

### Step 5: Find 40% of \( x \)
Now that we have the value of \( x \), we can find 40% of that number:
\[ 40\% \text{ of } x = 0.40 \times 965 \]

### Step 6: Calculate 40% of \( x \)
Calculating this gives:
\[ 0.40 \times 965 = 386 \]

### Final Answer
Thus, 40% of the number is:
\[ \boxed{386} \]