Successive discounts of 10% and 30% are equivalent to a single discount of :

Options

A. `40%`
B. `35%`
C. `38%`
D. `37%`

Answer

To find the equivalent single discount for successive discounts of 10% and 30%, we can use the formula for successive discounts:

\[ \text{Single Discount} = x + y - \frac{x \cdot y}{100} \]

where \( x \) and \( y \) are the individual discounts.

### Step 1: Identify the discounts
Here, we have:
- \( x = 10\% \)
- \( y = 30\% \)

### Step 2: Substitute the values into the formula
Now, substitute \( x \) and \( y \) into the formula:

\[ \text{Single Discount} = 10 + 30 - \frac{10 \cdot 30}{100} \]

### Step 3: Calculate the product of the discounts
Calculate \( \frac{10 \cdot 30}{100} \):

\[ 10 \cdot 30 = 300 \]
\[ \frac{300}{100} = 3 \]

### Step 4: Substitute back into the equation
Now substitute this value back into the equation:

\[ \text{Single Discount} = 10 + 30 - 3 \]

### Step 5: Perform the addition and subtraction
Now perform the addition and subtraction:

\[ \text{Single Discount} = 40 - 3 = 37 \]

### Final Answer
Thus, the equivalent single discount is:

\[ \text{Single Discount} = 37\% \]

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