What is effective discount of 4 successive discounts of 20% each ?

Options

A. `40.96%`
B. `64%`
C. `48%`
D. `59.04%`

Answer

To find the effective discount of 4 successive discounts of 20% each, we can follow these steps:

### Step 1: Understand the concept of successive discounts
When applying successive discounts, the total discount is not simply the sum of the individual discounts. Instead, we need to calculate the cumulative effect of each discount on the remaining amount after each discount is applied.

**Hint:** Remember that each discount is applied to the remaining amount after the previous discount.

### Step 2: Calculate the first two successive discounts
1. The first discount of 20% means you pay 80% of the original price.
2. After the first discount, the remaining amount is \(100\% - 20\% = 80\%\).
3. The second discount of 20% is applied to this remaining amount:
\[ \text{Effective amount after second discount} = 80\% \times (100\% - 20\%) = 80\% \times 80\% = 64\% \]
4. The cumulative discount after the first two discounts is:
\[ \text{Cumulative discount} = 100\% - 64\% = 36\% \]

**Hint:** Use the formula for cumulative discount: \(D = D_1 + D_2 - \left(\frac{D_1 \times D_2}{100}\right)\).

### Step 3: Calculate the third discount
1. Now, apply the third discount of 20% to the remaining amount after the first two discounts:
\[ \text{Effective amount after third discount} = 64\% \times (100\% - 20\%) = 64\% \times 80\% = 51.2\% \]
2. The cumulative discount after three discounts is:
\[ \text{Cumulative discount} = 100\% - 51.2\% = 48.8\% \]

**Hint:** Again, apply the discount to the amount remaining after previous discounts.

### Step 4: Calculate the fourth discount
1. Finally, apply the fourth discount of 20% to the remaining amount after the first three discounts:
\[ \text{Effective amount after fourth discount} = 51.2\% \times (100\% - 20\%) = 51.2\% \times 80\% = 40.96\% \]
2. The cumulative discount after four discounts is:
\[ \text{Cumulative discount} = 100\% - 40.96\% = 59.04\% \]

**Hint:** Always apply the discount to the amount remaining after all previous discounts have been applied.

### Final Answer
The effective discount after applying four successive discounts of 20% each is **59.04%**.