Three merchants. A, B and C. sell sewing machines at the same list price. Merchant A allows two successive discounts of 30% and 16% merchant B allows two successive discounts of 20% and 26% and merchant C allows two successive discounts of 25% and 20%. Which merchant should a customer choose to get the maximum discount?

Options

A. Merchant B
B. Merchant A
C. Merchant C
D. Either merchant B or merchant C

Answer

To determine which merchant offers the maximum discount, we can use the formula for calculating the effective discount when two successive discounts are applied. The formula is:

\[ \text{Effective Discount} = x + y - \frac{xy}{100} \]

where \(x\) and \(y\) are the two successive discounts.

### Step 1: Calculate the effective discount for Merchant A
Merchant A offers discounts of 30% and 16%.

Using the formula:
- \(x = 30\)
- \(y = 16\)

\[ \text{Effective Discount for A} = 30 + 16 - \frac{30 \times 16}{100} \]

Calculating:
\[ = 30 + 16 - \frac{480}{100} \]
\[ = 46 - 4.8 = 41.2\% \]

### Step 2: Calculate the effective discount for Merchant B
Merchant B offers discounts of 20% and 26%.

Using the formula:
- \(x = 20\)
- \(y = 26\)

\[ \text{Effective Discount for B} = 20 + 26 - \frac{20 \times 26}{100} \]

Calculating:
\[ = 20 + 26 - \frac{520}{100} \]
\[ = 46 - 5.2 = 40.8\% \]

### Step 3: Calculate the effective discount for Merchant C
Merchant C offers discounts of 25% and 20%.

Using the formula:
- \(x = 25\)
- \(y = 20\)

\[ \text{Effective Discount for C} = 25 + 20 - \frac{25 \times 20}{100} \]

Calculating:
\[ = 25 + 20 - \frac{500}{100} \]
\[ = 45 - 5 = 40\% \]

### Step 4: Compare the effective discounts
- Effective Discount for A: 41.2%
- Effective Discount for B: 40.8%
- Effective Discount for C: 40%

### Conclusion
Merchant A offers the maximum effective discount of 41.2%. Therefore, a customer should choose Merchant A to get the maximum discount.

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