A discount series of `10%,20%and40%` is equal to a single discount of

Options

A. `50%`
B. `56.80%`
C. `60%`
D. `70.28%`

Answer

To find the single equivalent discount of a series of discounts of 10%, 20%, and 40%, we can follow these steps:

### Step-by-Step Solution:

1. **Assume the Original Price**:
Let's assume the original price of the item is ₹100.

2. **Calculate the Price After the First Discount (10%)**:
- The first discount is 10% of ₹100.
- Discount amount = 10% of 100 = (10/100) * 100 = ₹10.
- Price after the first discount = Original Price - Discount = 100 - 10 = ₹90.

3. **Calculate the Price After the Second Discount (20%)**:
- The second discount is 20% of the new price (₹90).
- Discount amount = 20% of 90 = (20/100) * 90 = ₹18.
- Price after the second discount = Previous Price - Discount = 90 - 18 = ₹72.

4. **Calculate the Price After the Third Discount (40%)**:
- The third discount is 40% of the new price (₹72).
- Discount amount = 40% of 72 = (40/100) * 72 = ₹28.8.
- Price after the third discount = Previous Price - Discount = 72 - 28.8 = ₹43.2.

5. **Calculate the Total Discount**:
- The total discount from the original price of ₹100 to the final price of ₹43.2 is:
- Total Discount = Original Price - Final Price = 100 - 43.2 = ₹56.8.

6. **Calculate the Single Equivalent Discount Percentage**:
- The single equivalent discount percentage can be calculated as:
- Equivalent Discount Percentage = (Total Discount / Original Price) * 100
- Equivalent Discount Percentage = (56.8 / 100) * 100 = 56.8%.

### Final Answer:
The single equivalent discount of a series of discounts of 10%, 20%, and 40% is **56.8%**.

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