Out of the following, which is the best discount for a customer ?
I. 50% + 50% off
II. 60% + 40% off
III. 70% + 30% off
IV. Buy I get 4

Options

A. Only I and IV
B. Only II
C. Only I, II and III
D. Only III

Answer

To determine the best discount for a customer among the given options, we will analyze each discount scenario step by step.

### Step 1: Define the Selling Price
Assume the selling price of the item is \( X \).

### Step 2: Calculate the Effective Price for Each Discount Option

**Option I: 50% + 50% off**
1. First discount: 50% off means you pay 50% of the price.
\[ \text{Price after first discount} = 0.5X \]
2. Second discount: 50% off the new price.
\[ \text{Price after second discount} = 0.5 \times (0.5X) = 0.25X \]

**Option II: 60% + 40% off**
1. First discount: 60% off means you pay 40% of the price.
\[ \text{Price after first discount} = 0.4X \]
2. Second discount: 40% off the new price.
\[ \text{Price after second discount} = 0.4 \times (0.4X) = 0.16X \]

**Option III: 70% + 30% off**
1. First discount: 70% off means you pay 30% of the price.
\[ \text{Price after first discount} = 0.3X \]
2. Second discount: 30% off the new price.
\[ \text{Price after second discount} = 0.3 \times (0.3X) = 0.09X \]

**Option IV: Buy 1 Get 4**
1. This means you pay for 1 item but receive 4 items. Therefore, the effective price per item is:
\[ \text{Effective price per item} = \frac{X}{4} = 0.25X \]

### Step 3: Compare the Effective Prices
Now we will compare the effective prices from each option:
- Option I: \( 0.25X \)
- Option II: \( 0.16X \)
- Option III: \( 0.09X \)
- Option IV: \( 0.25X \)

### Conclusion
The best discount for the customer is from **Option III**, which results in an effective price of \( 0.09X \).