An article is listed at Rs. 920. A customer pays Rs. 742.90 for it after getting two successive discounts. If the rate of first discount is 15%, the rate of 2nd discount is

Options

A. 0.03
B. 0.05
C. 0.08
D. 0.12

Answer

To solve the problem step by step, we will follow the logical sequence of calculations as outlined in the video transcript.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Listed Price of the article (L) = Rs. 920
- Price paid by the customer (P) = Rs. 742.90
- First discount rate (D1) = 15%

2. **Calculate the Total Discount:**
- Total Discount (TD) = Listed Price - Price Paid
\[ TD = 920 - 742.90 = 177.10 \]

3. **Calculate the Amount of First Discount:**
- First Discount Amount (DA1) = 15% of Listed Price
\[ DA1 = \frac{15}{100} \times 920 = 138 \]

4. **Calculate the Price After the First Discount:**
- Price after First Discount (P1) = Listed Price - First Discount Amount
\[ P1 = 920 - 138 = 782 \]

5. **Calculate the Remaining Discount:**
- Remaining Discount (RD) = Total Discount - First Discount Amount
\[ RD = 177.10 - 138 = 39.10 \]

6. **Set Up the Equation for the Second Discount:**
- Let the second discount rate be x%. The amount of the second discount (DA2) can be expressed as:
\[ DA2 = \frac{x}{100} \times 782 \]
- From the previous step, we know that DA2 = Remaining Discount (39.10):
\[ \frac{x}{100} \times 782 = 39.10 \]

7. **Solve for x:**
- Rearranging the equation gives:
\[ x = \frac{39.10 \times 100}{782} \]
- Calculating the value:
\[ x = \frac{3910}{782} \approx 5 \]

8. **Conclusion:**
- The rate of the second discount (x) is 5%.

### Final Answer:
The rate of the second discount is **5%**.