Giving two successive discounts of 40% is equal to giving one discount of---------------------%

Options

A. a)0.8
B. b)0.96
C. c)0.64
D. d)0.72

Answer

To find the equivalent single discount for two successive discounts of 40%, we can follow these steps:

### Step 1: Understand the concept of successive discounts
When two successive discounts are applied, the final price is not simply the sum of the discounts. Instead, each discount is applied to the price after the previous discount.

### Step 2: Calculate the price after the first discount
Let the original price of the item be \( P \).

After the first discount of 40%, the price becomes:
\[ P_1 = P - (0.40 \times P) = P(1 - 0.40) = P(0.60) \]

### Step 3: Calculate the price after the second discount
Now, we apply the second discount of 40% on the new price \( P_1 \):
\[ P_2 = P_1 - (0.40 \times P_1) = P_1(1 - 0.40) = P(0.60)(0.60) = P(0.36) \]

### Step 4: Determine the equivalent single discount
The final price after both discounts is \( P(0.36) \). To find the equivalent single discount, we compare this final price to the original price \( P \):
\[ \text{Equivalent single discount} = 1 - \frac{P(0.36)}{P} = 1 - 0.36 = 0.64 \]

### Step 5: Convert to percentage
To express this as a percentage:
\[ \text{Equivalent single discount} = 0.64 \times 100\% = 64\% \]

### Final Answer
Therefore, giving two successive discounts of 40% is equal to giving one discount of **64%**.

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