If two successive discounts of 30% and 10% are given, then what will be the ratio of marked price to selling price?

Options

A. `50:21`
B. `25:9`
C. `100:63`
D. `25:21`

Answer

To find the ratio of the marked price (MP) to the selling price (SP) after applying two successive discounts of 30% and 10%, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Discounts**:
- The first discount is 30%.
- The second discount is 10%.

2. **Assuming the Marked Price**:
- Let the marked price (MP) be 100 (this simplifies calculations).

3. **Calculating the Selling Price after the First Discount**:
- After a 30% discount, the selling price becomes:
\[ SP_1 = MP - (30\% \text{ of } MP) = 100 - (0.30 \times 100) = 100 - 30 = 70 \]

4. **Calculating the Selling Price after the Second Discount**:
- Now, we apply the second discount of 10% on the new selling price (SP_1 = 70):
\[ SP_2 = SP_1 - (10\% \text{ of } SP_1) = 70 - (0.10 \times 70) = 70 - 7 = 63 \]

5. **Finding the Ratio of Marked Price to Selling Price**:
- Now, we have:
- Marked Price (MP) = 100
- Final Selling Price (SP) = 63
- The ratio of marked price to selling price is:
\[ \text{Ratio} = \frac{MP}{SP} = \frac{100}{63} \]

6. **Final Answer**:
- The ratio of marked price to selling price is \( 100 : 63 \).