A shopkeeper allows a discount of `10%` on his goods. For cash payments he further allows a discount of `20%` Find a single discount equivalent of the above offer.

Options

A. 25%
B. 28%
C. 32%
D. 35%

Answer

To find the single discount equivalent of a 10% discount followed by an additional 20% discount on the reduced price, we can follow these steps:

### Step-by-Step Solution:

1. **Assume the Marked Price (MP)**:
Let's assume the marked price of the goods is ₹100.

**Hint**: Start with a simple value for the marked price to make calculations easier.

2. **Calculate the Selling Price after the First Discount**:
The first discount is 10%. Therefore, the selling price after the first discount can be calculated as:
\[ \text{Selling Price after 10% discount} = \text{MP} - \text{10% of MP} = 100 - (10/100) \times 100 = 100 - 10 = ₹90 \]

**Hint**: To find the selling price after a discount, subtract the discount amount from the marked price.

3. **Calculate the Selling Price after the Second Discount**:
The second discount is 20% on the new selling price (₹90). Thus, the selling price after the second discount is:
\[ \text{Selling Price after 20% discount} = 90 - (20/100) \times 90 = 90 - 18 = ₹72 \]

**Hint**: Again, subtract the second discount from the selling price obtained after the first discount.

4. **Calculate the Total Discount Given**:
The total discount given from the original marked price (₹100) to the final selling price (₹72) is:
\[ \text{Total Discount} = \text{MP} - \text{Final Selling Price} = 100 - 72 = ₹28 \]

**Hint**: The total discount is simply the difference between the marked price and the final selling price.

5. **Calculate the Single Discount Rate**:
To find the single discount rate, we can use the formula:
\[ \text{Single Discount Rate} = \left(\frac{\text{Total Discount}}{\text{MP}}\right) \times 100 = \left(\frac{28}{100}\right) \times 100 = 28\% \]

**Hint**: The single discount rate is the total discount expressed as a percentage of the marked price.

### Final Answer:
The single discount equivalent of the above offer is **28%**.