The marked price of a shirt is Rs 150. After allowing two successive discounts its price is Rs 105. If second discount is 12.5% find the first discount.

Options

A. 0.1
B. 0.15
C. 0.2
D. 0.4

Answer

To solve the problem step by step, we will follow these calculations:

1. **Identify the Marked Price (MP)**:
The marked price of the shirt is given as Rs 150.
\[ \text{MP} = 150 \]

2. **Identify the Final Selling Price (SP)**:
After allowing two successive discounts, the final price is Rs 105.
\[ \text{SP} = 105 \]

3. **Identify the Second Discount**:
The second discount is given as 12.5%. We can express this as a fraction:
\[ \text{Second Discount} = \frac{12.5}{100} = \frac{1}{8} \]

4. **Calculate the Selling Price after the Second Discount (SP1)**:
The selling price after the first discount (SP1) can be calculated using the second discount:
\[ \text{SP} = \text{SP1} \times \left(1 - \frac{1}{8}\right) \]
This means:
\[ 105 = \text{SP1} \times \frac{7}{8} \]
To find SP1, we rearrange the equation:
\[ \text{SP1} = 105 \times \frac{8}{7} \]
Now, calculate SP1:
\[ \text{SP1} = 105 \times \frac{8}{7} = 105 \times 1.142857 \approx 120 \]

5. **Calculate the First Discount**:
Now we can find the first discount using the formula:
\[ \text{First Discount} = \text{MP} - \text{SP1} \]
Substitute the values:
\[ \text{First Discount} = 150 - 120 = 30 \]

6. **Calculate the Percentage of the First Discount**:
To find the percentage of the first discount:
\[ \text{First Discount Percentage} = \left(\frac{\text{First Discount}}{\text{MP}}\right) \times 100 \]
Substitute the values:
\[ \text{First Discount Percentage} = \left(\frac{30}{150}\right) \times 100 = 20\% \]

Thus, the first discount is **20%**.