`3/4`of the marked price of an article is equal to `5/6` th of selling price What is the discount percent.

Options

A. 12.5
B. 10
C. 15
D. 11.11

Answer

To solve the problem, we need to find the discount percentage given that \( \frac{3}{4} \) of the marked price (MP) is equal to \( \frac{5}{6} \) of the selling price (SP).

### Step-by-Step Solution:

1. **Set Up the Equation:**
We know that:
\[ \frac{3}{4} \text{ MP} = \frac{5}{6} \text{ SP} \]

2. **Cross Multiply to Find the Ratio of SP to MP:**
Rearranging the equation gives us:
\[ \text{SP} = \frac{3}{4} \cdot \frac{6}{5} \text{ MP} \]
This simplifies to:
\[ \text{SP} = \frac{3 \times 6}{4 \times 5} \text{ MP} = \frac{18}{20} \text{ MP} = \frac{9}{10} \text{ MP} \]

3. **Calculate the Discount:**
The discount (D) is given by:
\[ D = \text{MP} - \text{SP} \]
Substituting the value of SP:
\[ D = \text{MP} - \frac{9}{10} \text{ MP} = \frac{1}{10} \text{ MP} \]

4. **Calculate the Discount Percentage:**
The discount percentage (DP) is calculated as:
\[ \text{DP} = \left( \frac{D}{\text{MP}} \right) \times 100 \]
Substituting the value of D:
\[ \text{DP} = \left( \frac{\frac{1}{10} \text{ MP}}{\text{MP}} \right) \times 100 = \frac{1}{10} \times 100 = 10\% \]

### Conclusion:
The discount percentage is \( 10\% \).