10% discount and then 20% discount in succession is equivalent to total discount of .

Options

A. 0.15
B. 0.3
C. 0.24
D. 0.28

Explanation

To find the equivalent total discount when a 10% discount is followed by a 20% discount, we can use the formula for successive discounts. Let's solve the problem step by step.

### Step 1: Understand the Discounts
First, we need to understand that the discounts are applied successively. This means that the second discount is applied to the price after the first discount has been taken off.

### Step 2: Define the Discounts
Let:
- The first discount (x) = 10%
- The second discount (y) = 20%

### Step 3: Use the Formula for Successive Discounts
The formula for calculating the equivalent total discount when two discounts are applied successively is:
\[ \text{Total Discount} = x + y - \left(\frac{x \cdot y}{100}\right) \]

### Step 4: Substitute the Values
Now, substitute the values of x and y into the formula:
\[ \text{Total Discount} = 10 + 20 - \left(\frac{10 \cdot 20}{100}\right) \]

### Step 5: Calculate the Product of x and y
Calculate \( \frac{10 \cdot 20}{100} \):
\[ \frac{10 \cdot 20}{100} = \frac{200}{100} = 2 \]

### Step 6: Calculate the Total Discount
Now, substitute this value back into the total discount formula:
\[ \text{Total Discount} = 10 + 20 - 2 = 28 \]

### Step 7: Final Result
Thus, the equivalent total discount is:
\[ \text{Total Discount} = 28\% \]

### Summary
The equivalent total discount when a 10% discount is followed by a 20% discount is **28%**.

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