A man gets a discount 35% and then 12% on his food bill. How much equivalent single discount does he get?

Options

A. `42.8%`
B. `42.6%`
C. `41.9%`
D. `44.7%`

Answer

To find the equivalent single discount when a man receives two successive discounts of 35% and 12%, we can use the formula for successive discounts:

\[ \text{Equivalent Single Discount} = A + B - \frac{AB}{100} \]

Where:
- \( A \) is the first discount percentage (35%),
- \( B \) is the second discount percentage (12%).

### Step-by-Step Solution:

1. **Identify the Discounts**:
- First discount (A) = 35%
- Second discount (B) = 12%

2. **Apply the Successive Discount Formula**:
\[ \text{Equivalent Single Discount} = A + B - \frac{AB}{100} \]

3. **Substitute the Values**:
\[ \text{Equivalent Single Discount} = 35 + 12 - \frac{35 \times 12}{100} \]

4. **Calculate \( AB \)**:
\[ AB = 35 \times 12 = 420 \]

5. **Substitute \( AB \) into the Formula**:
\[ \text{Equivalent Single Discount} = 35 + 12 - \frac{420}{100} \]

6. **Calculate \( \frac{420}{100} \)**:
\[ \frac{420}{100} = 4.2 \]

7. **Final Calculation**:
\[ \text{Equivalent Single Discount} = 35 + 12 - 4.2 = 47 - 4.2 = 42.8 \]

8. **Conclusion**:
The equivalent single discount is **42.8%**.