A book is sold at three successive discounts of 20% , 20% and 10%. What is the net discount (in per cent) ?

Options

A. `42.4`
B. `48.6`
C. `44.2`
D. `40.4`

Answer

To find the net discount when a book is sold at three successive discounts of 20%, 20%, and 10%, we can use the formula for successive discounts. Here’s the step-by-step solution:

### Step 1: Understand the Discounts
We have three successive discounts:
- First discount (A) = 20%
- Second discount (B) = 20%
- Third discount (C) = 10%

### Step 2: Apply the Successive Discount Formula
The formula to calculate the net discount when applying successive discounts is:
\[ \text{Net Discount} = 100 - \left( (100 - A) \times (100 - B) \times (100 - C) \right) / 100^2 \]

### Step 3: Substitute the Values
Substituting the values of A, B, and C into the formula:
\[ \text{Net Discount} = 100 - \left( (100 - 20) \times (100 - 20) \times (100 - 10) \right) / 100^2 \]
\[ = 100 - \left( 80 \times 80 \times 90 \right) / 100^2 \]

### Step 4: Calculate the Products
Calculating the product:
\[ 80 \times 80 = 6400 \]
\[ 6400 \times 90 = 576000 \]

### Step 5: Divide by 10000
Now, divide by \(100^2 = 10000\):
\[ \frac{576000}{10000} = 57.6 \]

### Step 6: Calculate the Net Discount
Now, substitute this back into the net discount formula:
\[ \text{Net Discount} = 100 - 57.6 = 42.4\% \]

### Final Answer
Thus, the net discount is **42.4%**.

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