The difference between 52% of a number and 34% of the same number is 135. What is 76% of that number ?

Options

A. 525
B. 600
C. 550
D. 570

Answer

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

### Step 1: Define the variable
Let the number be represented as \( x \).

### Step 2: Set up the equation based on the problem statement
According to the problem, the difference between 52% of the number and 34% of the same number is 135. We can express this mathematically as:
\[ 0.52x - 0.34x = 135 \]

### Step 3: Simplify the equation
Combine the percentages on the left side:
\[ (0.52 - 0.34)x = 135 \]
\[ 0.18x = 135 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides of the equation by 0.18:
\[ x = \frac{135}{0.18} \]
Calculating this gives:
\[ x = 750 \]

### Step 5: Calculate 76% of the number
Now that we have \( x = 750 \), we need to find 76% of this number:
\[ 0.76x = 0.76 \times 750 \]
Calculating this gives:
\[ 0.76 \times 750 = 570 \]

### Final Answer
Thus, 76% of the number is \( \boxed{570} \).

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