Ram Naresh got two successive discounts, a bag with a list price of Rs. 400 is available at Rs. 160. If the second discount is 20%, find the first discount.
A. 40%
B. 30%
C. 50%
D. 80%

Options

A. D
B. B
C. A
D. C

Answer

To find the first discount given the list price, the final price after two successive discounts, and the second discount percentage, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- List Price (LP) = Rs. 400
- Final Price (FP) = Rs. 160
- Second Discount (D2) = 20%

2. **Calculate the price after the second discount:**
- The second discount of 20% means that the price after the first discount (P1) is reduced by 20%.
- Therefore, we can express this as:
\[ P1 = FP / (1 - D2) \]
- Substituting the values:
\[ P1 = 160 / (1 - 0.20) = 160 / 0.80 = 200 \]

3. **Calculate the first discount:**
- Now we know the price after the first discount (P1) is Rs. 200.
- The first discount (D1) can be calculated using the formula:
\[ D1 = (LP - P1) / LP \times 100 \]
- Substituting the values:
\[ D1 = (400 - 200) / 400 \times 100 = 200 / 400 \times 100 = 50\% \]

4. **Conclusion:**
- The first discount is 50%.

### Final Answer:
- The first discount is **50%** (Option C).