The difference between 81% and 49% of a number is 768. What is the 48% of the number?

Options

A. 1186
B. 1248
C. 1152
D. 1168

Answer

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

### Step 1: Set up the equation based on the problem statement.
The problem states that the difference between 81% and 49% of a number is 768. We can express this mathematically as:
\[ 81\% \text{ of } x - 49\% \text{ of } x = 768 \]
This can be rewritten as:
\[ (81\% - 49\%) \times x = 768 \]

### Step 2: Calculate the difference in percentages.
Now, let's calculate \( 81\% - 49\% \):
\[ 81\% - 49\% = 32\% \]
So, we can substitute this back into our equation:
\[ 32\% \text{ of } x = 768 \]

### Step 3: Convert the percentage to a decimal and solve for \( x \).
Now, we can express \( 32\% \) as a decimal:
\[ 32\% = \frac{32}{100} = 0.32 \]
Thus, we have:
\[ 0.32x = 768 \]
To find \( x \), we divide both sides by \( 0.32 \):
\[ x = \frac{768}{0.32} \]

### Step 4: Perform the division.
Calculating \( \frac{768}{0.32} \):
\[ x = 768 \div 0.32 = 2400 \]

### Step 5: Calculate 48% of the number \( x \).
Now that we have found \( x = 2400 \), we need to calculate \( 48\% \) of \( x \):
\[ 48\% \text{ of } 2400 = \frac{48}{100} \times 2400 \]
This simplifies to:
\[ = 0.48 \times 2400 \]

### Step 6: Perform the multiplication.
Calculating \( 0.48 \times 2400 \):
\[ = 48 \times 24 = 1152 \]

### Final Answer:
Thus, \( 48\% \) of the number is \( 1152 \).

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