If two T-shirts are offered free on purchase of five T-shirts, what is the effective discount (in %) on each T-shirt?

Options

A. 40
B. 20
C. 30
D. 50

Answer

To find the effective discount on each T-shirt when two T-shirts are offered free on the purchase of five T-shirts, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Mark Price of Each T-shirt:**
Let's assume the mark price of each T-shirt is ₹100.

2. **Calculate the Total Mark Price for 5 T-shirts:**
If the mark price of each T-shirt is ₹100, then the total mark price for 5 T-shirts is:
\[ \text{Total Mark Price for 5 T-shirts} = 5 \times 100 = ₹500 \]

3. **Calculate the Mark Price of the Free T-shirts:**
Since 2 T-shirts are offered for free, the total mark price for these 2 T-shirts is:
\[ \text{Total Mark Price for 2 Free T-shirts} = 2 \times 100 = ₹200 \]

4. **Calculate the Total Value of T-shirts Received:**
When you purchase 5 T-shirts and receive 2 additional T-shirts for free, the total number of T-shirts you receive is:
\[ \text{Total T-shirts} = 5 + 2 = 7 \]
The total value of all T-shirts (including the free ones) is:
\[ \text{Total Value} = \text{Total Mark Price for 5 T-shirts} + \text{Total Mark Price for 2 Free T-shirts} = 500 + 200 = ₹700 \]

5. **Calculate the Effective Price per T-shirt:**
The effective price per T-shirt when you consider the total value of the T-shirts received is:
\[ \text{Effective Price per T-shirt} = \frac{\text{Total Price Paid}}{\text{Total T-shirts}} = \frac{500}{7} \approx ₹71.43 \]

6. **Calculate the Discount on Each T-shirt:**
The discount on each T-shirt can be calculated as:
\[ \text{Discount per T-shirt} = \text{Mark Price} - \text{Effective Price} = 100 - 71.43 \approx ₹28.57 \]

7. **Calculate the Effective Discount Percentage:**
The effective discount percentage can be calculated as:
\[ \text{Effective Discount Percentage} = \left( \frac{\text{Discount per T-shirt}}{\text{Mark Price}} \right) \times 100 = \left( \frac{28.57}{100} \right) \times 100 \approx 28.57\% \]

### Final Answer:
The effective discount on each T-shirt is approximately **28.57%**.