Dolly goes to a shop to purchase a doll priced at Rs. 400. She is offered 4 discount options by the shopkeeper. Which of these options should she opt for to gain maximum advantage of the discount offered?

Options

A. Single discount of 30%
B. 2 successive discounts of 15% each
C. 2 successive discounts of 20% and 10%
D. 2 successive discounts of 20% and 12%

Answer

To determine which discount option Dolly should choose to maximize her savings on the doll priced at Rs. 400, we will calculate the effective discount for each of the four options provided by the shopkeeper.

### Step-by-Step Solution:

1. **Identify the Discount Options**:
- Option A: 30% discount
- Option B: Two successive discounts of 15% each
- Option C: Two successive discounts of 20% and 10%
- Option D: Two successive discounts of 20% and 12%

2. **Calculate the Effective Discount for Each Option**:

**Option A**:
- Discount = 30%
- Effective Price = Price - (30% of Price)
- Effective Price = 400 - (0.30 × 400) = 400 - 120 = Rs. 280
- Effective Discount = 30%

**Option B**:
- Successive Discounts = 15% and 15%
- Using the formula: Effective Discount = x + y - (xy/100)
- Here, x = 15 and y = 15
- Effective Discount = 15 + 15 - (15 × 15 / 100) = 30 - 2.25 = 27.75%
- Effective Price = 400 - (27.75% of 400) = 400 - 111 = Rs. 289

**Option C**:
- Successive Discounts = 20% and 10%
- Using the formula: Effective Discount = x + y - (xy/100)
- Here, x = 20 and y = 10
- Effective Discount = 20 + 10 - (20 × 10 / 100) = 30 - 2 = 28%
- Effective Price = 400 - (28% of 400) = 400 - 112 = Rs. 288

**Option D**:
- Successive Discounts = 20% and 12%
- Using the formula: Effective Discount = x + y - (xy/100)
- Here, x = 20 and y = 12
- Effective Discount = 20 + 12 - (20 × 12 / 100) = 32 - 2.4 = 29.6%
- Effective Price = 400 - (29.6% of 400) = 400 - 118.4 = Rs. 281.6

3. **Compare the Effective Discounts**:
- Option A: 30%
- Option B: 27.75%
- Option C: 28%
- Option D: 29.6%

4. **Conclusion**:
The maximum effective discount is from Option A, which offers a 30% discount. Therefore, Dolly should opt for Option A to gain the maximum advantage.

### Summary of Effective Discounts:
- Option A: 30%
- Option B: 27.75%
- Option C: 28%
- Option D: 29.6%

### Final Answer:
Dolly should choose **Option A** for the maximum discount of **30%**.

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