What will be a single equivalent discount for successive discounts of 10% and 5% on marked price of an article?

Answer

To find the single equivalent discount for successive discounts of 10% and 5%, we can follow these steps:

### Step 1: Identify the Discounts
We have two successive discounts:
- Discount 1 (D1) = 10%
- Discount 2 (D2) = 5%

### Step 2: Use the Formula for Single Equivalent Discount
The formula for calculating the single equivalent discount (D) when two successive discounts are applied is:
\[ D = D1 + D2 - \left(\frac{D1 \times D2}{100}\right) \]

### Step 3: Substitute the Values into the Formula
Substituting the values of D1 and D2 into the formula:
\[ D = 10 + 5 - \left(\frac{10 \times 5}{100}\right) \]

### Step 4: Calculate the Product of the Discounts
Calculate the product of D1 and D2:
\[ 10 \times 5 = 50 \]

### Step 5: Divide by 100
Now, divide the product by 100:
\[ \frac{50}{100} = 0.5 \]

### Step 6: Substitute Back into the Formula
Now substitute this value back into the formula:
\[ D = 10 + 5 - 0.5 \]

### Step 7: Perform the Addition and Subtraction
Now, calculate the final value:
\[ D = 15 - 0.5 = 14.5 \]

### Step 8: Convert to Percentage
The single equivalent discount is:
\[ D = 14.5\% \]

Thus, the single equivalent discount for successive discounts of 10% and 5% is **14.5%**.

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