Two dealers X and Y selling the same model of refrigerator mark them under the same selling prices. X gives successive discounts of 25% and 5% and Y gives successive discounts of 16% and 12%. From whom is it more profitable to purchase the refrigerator?

Options

A. Form Y
B. From X
C. Indifferent between the two
D. Cannot be determined

Answer

To determine from whom it is more profitable to purchase the refrigerator, we need to calculate the effective discount offered by both dealers, X and Y, based on their successive discounts.

### Step-by-Step Solution:

1. **Identify the Discounts**:
- Dealer X offers discounts of 25% and 5%.
- Dealer Y offers discounts of 16% and 12%.

2. **Calculate the Effective Discount for Dealer X**:
- The formula for calculating the effective discount when two successive discounts A% and B% are given is:
\[ \text{Effective Discount} = 100 - \left(100 - A\right) \times \left(100 - B\right) / 100 \]
- For Dealer X:
- A = 25%
- B = 5%
- Calculate:
\[ \text{Effective Discount for X} = 100 - \left(100 - 25\right) \times \left(100 - 5\right) / 100 \]
\[ = 100 - 75 \times 95 / 100 \]
\[ = 100 - 71.25 \]
\[ = 28.75\% \]

3. **Calculate the Effective Discount for Dealer Y**:
- For Dealer Y:
- A = 16%
- B = 12%
- Calculate:
\[ \text{Effective Discount for Y} = 100 - \left(100 - 16\right) \times \left(100 - 12\right) / 100 \]
\[ = 100 - 84 \times 88 / 100 \]
\[ = 100 - 73.92 \]
\[ = 26.08\% \]

4. **Compare the Effective Discounts**:
- Effective Discount from Dealer X = 28.75%
- Effective Discount from Dealer Y = 26.08%
- Since 28.75% > 26.08%, Dealer X offers a better discount.

5. **Conclusion**:
- It is more profitable to purchase the refrigerator from Dealer X.