Find the single discount equivalent to successive discount of 20% and 10%

Answer

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

### Step-by-Step Solution:

1. **Assume the Cost Price**:
Let's assume the cost price of the item is ₹100. This makes calculations easier.

**Hint**: Start with a round number like 100 to simplify percentage calculations.

2. **Calculate the First Discount**:
The first discount is 20%.
- Calculate 20% of ₹100:
\[ \text{First Discount} = 20\% \text{ of } 100 = \frac{20}{100} \times 100 = ₹20 \]
- Subtract this discount from the original price:
\[ \text{Price after first discount} = 100 - 20 = ₹80 \]

**Hint**: Remember that a discount reduces the price, so subtract the discount from the original price.

3. **Calculate the Second Discount**:
The second discount is 10%, applied on the new price of ₹80.
- Calculate 10% of ₹80:
\[ \text{Second Discount} = 10\% \text{ of } 80 = \frac{10}{100} \times 80 = ₹8 \]
- Subtract this discount from the price after the first discount:
\[ \text{Final Price} = 80 - 8 = ₹72 \]

**Hint**: Always apply the second discount on the price after the first discount.

4. **Calculate the Total Discount**:
Now, we need to find the total discount given from the original price of ₹100 to the final price of ₹72.
- The total discount is:
\[ \text{Total Discount} = 100 - 72 = ₹28 \]

**Hint**: The total discount is the difference between the original price and the final price.

5. **Calculate the Single Discount Percentage**:
To find the single discount percentage, we can use the formula:
\[ \text{Single Discount Percentage} = \left(\frac{\text{Total Discount}}{\text{Original Price}}\right) \times 100 \]
- Plugging in the values:
\[ \text{Single Discount Percentage} = \left(\frac{28}{100}\right) \times 100 = 28\% \]

**Hint**: To find the percentage, divide the total discount by the original price and multiply by 100.

### Final Answer:
The single discount equivalent to successive discounts of 20% and 10% is **28%**.