Successive discounts of 10%, 20% and 30% ls equivalent to a single discount of

Options

A. 60%
B. `49.6 %`
C. `40.5 %`
D. `36%`

Answer

To find the single equivalent discount for successive discounts of 10%, 20%, and 30%, we can follow these steps:

### Step-by-Step Solution:

1. **Assume the MRP (Marked Price)**:
Let's assume the MRP (Marked Price) of the product is Rs 100.

2. **Calculate Selling Price after First Discount (10%)**:
- The first discount is 10%.
- Selling Price after the first discount (SP1) can be calculated as:
\[ SP1 = MRP \times \left(1 - \frac{D1}{100}\right) = 100 \times \left(1 - \frac{10}{100}\right) = 100 \times 0.90 = 90 \]

3. **Calculate Selling Price after Second Discount (20%)**:
- The second discount is 20%.
- Selling Price after the second discount (SP2) can be calculated as:
\[ SP2 = SP1 \times \left(1 - \frac{D2}{100}\right) = 90 \times \left(1 - \frac{20}{100}\right) = 90 \times 0.80 = 72 \]

4. **Calculate Selling Price after Third Discount (30%)**:
- The third discount is 30%.
- Selling Price after the third discount (SP3) can be calculated as:
\[ SP3 = SP2 \times \left(1 - \frac{D3}{100}\right) = 72 \times \left(1 - \frac{30}{100}\right) = 72 \times 0.70 = 50.4 \]

5. **Calculate the Single Equivalent Discount**:
- The single equivalent discount can be calculated using the formula:
\[ \text{Single Discount} = \frac{MRP - SP3}{MRP} \times 100 \]
- Substituting the values:
\[ \text{Single Discount} = \frac{100 - 50.4}{100} \times 100 = \frac{49.6}{100} \times 100 = 49.6\% \]

### Final Answer:
The single equivalent discount for successive discounts of 10%, 20%, and 30% is **49.6%**.

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