A single discount equivalent to three simple discounts of 10%, 12% and 15% is

Options

A. 32.68
B. 24.1
C. 37
D. 35.36

Answer

To find the single discount equivalent to three successive discounts of 10%, 12%, and 15%, we can use the formula for successive discounts.

### Step-by-Step Solution:

1. **Identify the Discounts:**
- Let the first discount \( A = 10\% \)
- Let the second discount \( B = 12\% \)
- Let the third discount \( C = 15\% \)

2. **Calculate the Equivalent Discount for the First Two Discounts:**
- Use the formula for two successive discounts:
\[ \text{Equivalent Discount} = A + B - \frac{A \times B}{100} \]
- Substitute \( A \) and \( B \):
\[ \text{Equivalent Discount} = 10 + 12 - \frac{10 \times 12}{100} \]
- Calculate \( \frac{10 \times 12}{100} = \frac{120}{100} = 1.2 \):
\[ \text{Equivalent Discount} = 10 + 12 - 1.2 = 22 - 1.2 = 20.8\% \]

3. **Calculate the Equivalent Discount Including the Third Discount:**
- Now, use the equivalent discount from the previous step and the third discount \( C \):
\[ \text{New Equivalent Discount} = 20.8 + 15 - \frac{20.8 \times 15}{100} \]
- Calculate \( \frac{20.8 \times 15}{100} = \frac{312}{100} = 3.12 \):
\[ \text{New Equivalent Discount} = 20.8 + 15 - 3.12 = 35.8 - 3.12 = 32.68\% \]

4. **Final Result:**
- The single discount equivalent to three successive discounts of 10%, 12%, and 15% is **32.68%**.