A tyre is sold at three successive discounts of 20%, 30% and 20%. What is the net discount (in percentage)?

Options

A. 62.8
B. 59.6
C. 55.2
D. 51.4

Explanation

To find the net discount after applying three successive discounts of 20%, 30%, and 20% on a tyre, we can use the formula for calculating the net percentage discount when two percentages are applied successively.

### Step-by-Step Solution:

1. **First Discount Calculation**:
- The first discount is 20%.
- Let the original price of the tyre be \( P \).
- After the first discount, the price becomes:
\[ P_1 = P - 0.20P = 0.80P \]

2. **Second Discount Calculation**:
- The second discount is 30% applied on the new price \( P_1 \).
- After the second discount, the price becomes:
\[ P_2 = P_1 - 0.30P_1 = 0.70P_1 = 0.70 \times 0.80P = 0.56P \]

3. **Third Discount Calculation**:
- The third discount is 20% applied on the new price \( P_2 \).
- After the third discount, the price becomes:
\[ P_3 = P_2 - 0.20P_2 = 0.80P_2 = 0.80 \times 0.56P = 0.448P \]

4. **Calculating the Net Discount**:
- The final price after all discounts is \( P_3 = 0.448P \).
- The net discount can be calculated as:
\[ \text{Net Discount} = \left(1 - \frac{P_3}{P}\right) \times 100 = \left(1 - 0.448\right) \times 100 = 0.552 \times 100 = 55.2\% \]

### Final Answer:
The net discount on the tyre is **55.2%**.