What is the single equivalent discount for successive discounts of 10%, 20% and 15% on marked price for motor bike?

Answer

To find the single equivalent discount for successive discounts of 10%, 20%, and 15%, we can follow these steps:

### Step 1: Identify the Discounts
Let:
- D1 = 10%
- D2 = 20%
- D3 = 15%

### Step 2: Calculate the Equivalent Discount for D1 and D2
To find the equivalent discount for D1 and D2, we use the formula:
\[ \text{Equivalent Discount} = D1 + D2 - \left(\frac{D1 \times D2}{100}\right) \]
Substituting the values:
\[ \text{Equivalent Discount} = 10 + 20 - \left(\frac{10 \times 20}{100}\right) \]
Calculating:
\[ = 30 - 2 = 28\% \]

### Step 3: Calculate the Equivalent Discount for D1, D2, and D3
Now we need to find the equivalent discount for the combined discount of 28% (from D1 and D2) and D3 (15%):
Using the same formula:
\[ \text{Total Equivalent Discount} = \text{Equivalent Discount from D1 and D2} + D3 - \left(\frac{\text{Equivalent Discount from D1 and D2} \times D3}{100}\right) \]
Substituting the values:
\[ \text{Total Equivalent Discount} = 28 + 15 - \left(\frac{28 \times 15}{100}\right) \]
Calculating:
\[ = 43 - \left(\frac{420}{100}\right) = 43 - 4.2 = 38.8\% \]

### Final Answer
The single equivalent discount for successive discounts of 10%, 20%, and 15% is **38.8%**.

---