Find a simple discount equivalent in a discount series of ` 10 %`, ` 20 %` and ` 25 %`.

Options

A. ` 55 %`
B. ` 45 %`
C. ` 52 %`
D. ` 46 %`

Answer

To find the simple discount equivalent to a series of discounts of 10%, 20%, and 25%, we can use the formula for calculating the equivalent single discount from multiple successive discounts.

### Step-by-Step Solution:

1. **Identify the Discounts**:
- Let the discounts be:
- \( d_1 = 10\% \)
- \( d_2 = 20\% \)
- \( d_3 = 25\% \)

2. **Convert Discounts to Decimal Form**:
- Convert the percentages to their decimal equivalents:
- \( d_1 = 0.10 \)
- \( d_2 = 0.20 \)
- \( d_3 = 0.25 \)

3. **Calculate the Remaining Amount After Each Discount**:
- The remaining amount after applying each discount can be calculated as follows:
- After the first discount:
\[ R_1 = 100 - d_1 = 100 - 10 = 90 \]
- After the second discount:
\[ R_2 = R_1 \times (1 - d_2) = 90 \times (1 - 0.20) = 90 \times 0.80 = 72 \]
- After the third discount:
\[ R_3 = R_2 \times (1 - d_3) = 72 \times (1 - 0.25) = 72 \times 0.75 = 54 \]

4. **Calculate the Final Remaining Amount**:
- The final remaining amount after all discounts is \( R_3 = 54 \).

5. **Calculate the Equivalent Single Discount**:
- The equivalent single discount can be calculated using the formula:
\[ \text{Equivalent Discount} = 100 - \left( \frac{R_3}{100} \times 100 \right) = 100 - 54 = 46 \]

6. **Conclusion**:
- The simple discount equivalent to the series of discounts of 10%, 20%, and 25% is **46%**.