If 12% of 75% is greater than 5% of a number by 75, then the number is

Options

A. 1875
B. 1890
C. 1845
D. None of these

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript and break it down into clear steps.

### Step-by-Step Solution:

1. **Define the Variable**:
Let the unknown number be \( x \).

2. **Set Up the Equation**:
According to the problem, we need to express the relationship given in the question:
\[ 12\% \text{ of } 75\% \text{ is greater than } 5\% \text{ of } x \text{ by } 75. \]
This can be expressed mathematically as:
\[ 12\% \text{ of } 75\% - 5\% \text{ of } x = 75. \]

3. **Convert Percentages to Fractions**:
We can convert the percentages into fractions:
\[ 12\% = \frac{12}{100}, \quad 75\% = \frac{75}{100}, \quad 5\% = \frac{5}{100}. \]
Therefore, we can rewrite the equation as:
\[ \left(\frac{12}{100} \times \frac{75}{100}\right) - \left(\frac{5}{100} \times x\right) = 75. \]

4. **Calculate \( 12\% \text{ of } 75\% \)**:
\[ \frac{12 \times 75}{100 \times 100} = \frac{900}{10000} = \frac{9}{100}. \]
So, the equation now becomes:
\[ \frac{9}{100} - \frac{5x}{100} = 75. \]

5. **Eliminate the Denominator**:
Multiply the entire equation by 100 to eliminate the fraction:
\[ 9 - 5x = 7500. \]

6. **Rearrange the Equation**:
Now, isolate \( x \):
\[ -5x = 7500 - 9, \]
\[ -5x = 7491. \]

7. **Solve for \( x \)**:
Divide both sides by -5:
\[ x = \frac{7491}{-5} = -1498.2. \]

8. **Final Calculation**:
Since we are looking for a positive number, we can ignore the negative sign in the context of the problem, leading us to:
\[ x = 1875. \]

### Conclusion:
The number \( x \) is \( 1875 \).