Which of the following will give maximum discount on Rs. 6896 ?
(a) 2 successive discounts of 5% and 5%
(b) Single discount of 10%
(c) 2 successive discounts of 8% and 2%

Question

Which of the following will give maximum discount on Rs. 6896 ? 
(a) 2 successive discounts of 5% and 5% 
(b) Single discount of 10% 
(c) 2 successive discounts of 8% and 2%

Accepted Answer

To determine which option provides the maximum discount on Rs. 6896, we need to calculate the effective discount for each option and compare them. The correct answer is given as Option 2, which is a single discount of 10%. Let's justify why this is correct and why the other options are not.

1. **Option 2: Single discount of 10%**
   - A single discount of 10% on Rs. 6896 is calculated as follows:
     $$
     \text{Discount} = \frac{10}{100} \times 6896 = 689.6
     $$
   - Therefore, the amount after the discount is:
     $$
     6896 - 689.6 = 6206.4
     $$
   - The discount amount is Rs. 689.6.

2. **Option 1: Two successive discounts of 5% and 5%**
   - First discount of 5%:
     $$
     \text{First discount} = \frac{5}{100} \times 6896 = 344.8
     $$
     $$
     \text{Amount after first discount} = 6896 - 344.8 = 6551.2
     $$
   - Second discount of 5% on the new amount:
     $$
     \text{Second discount} = \frac{5}{100} \times 6551.2 = 327.56
     $$
     $$
     \text{Total amount after both discounts} = 6551.2 - 327.56 = 6223.64
     $$
   - Total discount amount is:
     $$
     6896 - 6223.64 = 672.36
     $$
   - The discount amount is Rs. 672.36, which is less than Rs. 689.6.

3. **Option 3: Two successive discounts of 8% and 2%**
   - First discount of 8%:
     $$
     \text{First discount} = \frac{8}{100} \times 6896 = 551.68
     $$
     $$
     \text{Amount after first discount} = 6896 - 551.68 = 6344.32
     $$
   - Second discount of 2% on the new amount:
     $$
     \text{Second discount} = \frac{2}{100} \times 6344.32 = 126.89
     $$
     $$
     \text{Total amount after both discounts} = 6344.32 - 126.89 = 6217.43
     $$
   - Total discount amount is:
     $$
     6896 - 6217.43 = 678.57
     $$
   - The discount amount is Rs. 678.57, which is also less than Rs. 689.6.

In conclusion, the single discount of 10% (Option 2) provides the maximum discount of Rs. 689.6, which is greater than the discounts provided by the other options. Therefore, Option 2 is the correct answer.