Which single discount will be equal to two successive discounts of 12% and 5%?
A 17% B. 8.5% C. 16.4% D. 15.2%

Options

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

Answer

To find the single discount equivalent to two successive discounts of 12% and 5%, we can use the formula for calculating the equivalent single discount:

\[ \text{Single Equivalent Discount} = x + y - \frac{xy}{100} \]

where \(x\) and \(y\) are the two successive discounts.

### Step-by-Step Solution:

1. **Identify the Discounts**:
- Let \(x = 12\%\) (first discount)
- Let \(y = 5\%\) (second discount)

2. **Substitute the Values into the Formula**:
\[ \text{Single Equivalent Discount} = 12 + 5 - \frac{12 \times 5}{100} \]

3. **Calculate the Sum of the Discounts**:
\[ 12 + 5 = 17 \]

4. **Calculate the Product of the Discounts**:
\[ 12 \times 5 = 60 \]

5. **Divide the Product by 100**:
\[ \frac{60}{100} = 0.6 \]

6. **Subtract the Result from the Sum**:
\[ 17 - 0.6 = 16.4 \]

7. **Final Result**:
The single equivalent discount is \(16.4\%\).

### Conclusion:
The answer is \(16.4\%\), which corresponds to option C.

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