The discount series 10%, 20% 40% is equivalent to a single discount of

Options

A. `50%`
B. `56.8%`
C. `60%`
D. `62.28%`

Answer

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

### Step-by-Step Solution:

1. **Start with an Initial Amount**:
Let's assume the initial price of the item is ₹100.

2. **Apply the First Discount (40%)**:
- Calculate 40% of ₹100:
\[ 40\% \text{ of } 100 = \frac{40}{100} \times 100 = 40 \]
- Subtract this from the initial amount:
\[ 100 - 40 = 60 \]

3. **Apply the Second Discount (20%)**:
- Now, apply 20% on the new amount (₹60):
\[ 20\% \text{ of } 60 = \frac{20}{100} \times 60 = 12 \]
- Subtract this from ₹60:
\[ 60 - 12 = 48 \]

4. **Apply the Third Discount (10%)**:
- Now, apply 10% on the new amount (₹48):
\[ 10\% \text{ of } 48 = \frac{10}{100} \times 48 = 4.8 \]
- Subtract this from ₹48:
\[ 48 - 4.8 = 43.2 \]

5. **Calculate the Total Discount**:
- The final amount after all discounts is ₹43.2.
- The total discount given from the original ₹100 is:
\[ 100 - 43.2 = 56.8 \]

6. **Find the Equivalent Single Discount Percentage**:
- To find the equivalent single discount percentage:
\[ \text{Equivalent Discount} = \left(\frac{\text{Total Discount}}{\text{Original Price}}\right) \times 100 \]
- Substitute the values:
\[ \text{Equivalent Discount} = \left(\frac{56.8}{100}\right) \times 100 = 56.8\% \]

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

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