If the difference between discount of 50% and two successive discounts of `20%` on a certain bill is Rs 42, then what is the amount (in Rs) of the bill?

Options

A. a. 300
B. b. 750
C. c. 600
D. d. 800

Answer

To solve the problem, we need to find the amount of the bill given the difference between a single discount and two successive discounts.

### Step-by-Step Solution:

1. **Understanding Discounts**:
- The first discount (D1) is 50%.
- The second discount (D2) is two successive discounts of 20%.

2. **Calculating the Successive Discount**:
- To find the effective discount of two successive discounts of 20%, we use the formula:
\[ D2 = x + y - \frac{xy}{100} \]
where \(x = 20\) and \(y = 20\).
- Plugging in the values:
\[ D2 = 20 + 20 - \frac{20 \times 20}{100} \]
\[ D2 = 40 - \frac{400}{100} \]
\[ D2 = 40 - 4 = 36\% \]

3. **Finding the Difference Between Discounts**:
- The difference between the first discount (D1) and the second discount (D2) is given as Rs. 42:
\[ D1 - D2 = 42 \]
Substituting the values:
\[ 50\% - 36\% = 42 \]
\[ 14\% = 42 \]

4. **Calculating the Total Bill Amount**:
- If 14% of the bill is Rs. 42, we can find 100% of the bill using the proportion:
\[ \text{Let the total bill be } x. \]
\[ \frac{14}{100} \times x = 42 \]
- Rearranging gives:
\[ x = \frac{42 \times 100}{14} \]
- Simplifying:
\[ x = \frac{4200}{14} = 300 \]

5. **Conclusion**:
- The amount of the bill is Rs. 300.

### Final Answer:
The amount of the bill is Rs. 300.