A Brand offers three types of successive discounts:
(i) 25% and 15% (ii) 30% and 10% (iii) 35% and 5%
Which offer is the best for a customer ?

Options

A. First offer
B. Second offer
C. Third offer
D. All are equally

Answer

To determine which discount offer is the best for a customer, we will calculate the effective discount for each of the three offers using the formula for successive discounts.

### Step 1: Calculate the effective discount for the first offer (25% and 15%)

Using the formula for successive discounts:
\[ \text{Effective Discount} = x + y - \frac{xy}{100} \]
where \(x\) is the first discount and \(y\) is the second discount.

For the first offer:
- \(x = 25\%\)
- \(y = 15\%\)

Substituting the values into the formula:
\[ \text{Effective Discount} = 25 + 15 - \frac{25 \times 15}{100} \]
Calculating:
\[ = 40 - \frac{375}{100} \]
\[ = 40 - 3.75 = 36.25\% \]

### Step 2: Calculate the effective discount for the second offer (30% and 10%)

Using the same formula:
For the second offer:
- \(x = 30\%\)
- \(y = 10\%\)

Substituting the values into the formula:
\[ \text{Effective Discount} = 30 + 10 - \frac{30 \times 10}{100} \]
Calculating:
\[ = 40 - \frac{300}{100} \]
\[ = 40 - 3 = 37\% \]

### Step 3: Calculate the effective discount for the third offer (35% and 5%)

Using the same formula:
For the third offer:
- \(x = 35\%\)
- \(y = 5\%\)

Substituting the values into the formula:
\[ \text{Effective Discount} = 35 + 5 - \frac{35 \times 5}{100} \]
Calculating:
\[ = 40 - \frac{175}{100} \]
\[ = 40 - 1.75 = 38.25\% \]

### Step 4: Compare the effective discounts

Now we compare the effective discounts calculated:
1. First offer: 36.25%
2. Second offer: 37%
3. Third offer: 38.25%

### Conclusion

The best offer for the customer is the third offer, which provides an effective discount of **38.25%**.

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