A dinner set has a marked price of Rs 1500. A customer buys it after receiving two successive discounts: first a discount of 15% on the marked price and then an additional discount on the reduced price. If the customer finally pays Rs 1173, what was the rate of the second discount?

Introduction / Context:
This problem focuses on successive percentage discounts and how to find an unknown discount rate when the final selling price is known. It is a standard question in the percentage and discount chapter and tests algebraic manipulation along with a clear understanding that every discount is applied on the current price, not the original marked price.

Given Data / Assumptions:

• Marked price of the dinner set = Rs 1500.
• First discount = 15% on the marked price.
• Second discount = unknown percentage on the already reduced price.
• Final amount paid by the customer = Rs 1173.
• We assume no additional charges or taxes.

Concept / Approach:
The key idea is that the first discount reduces the marked price to a new intermediate price. The second discount is then applied on this intermediate price. We first compute the price after the first discount. Then we express the final price in terms of the unknown second discount and equate it to the given amount. Solving this linear equation gives the discount rate. We should remember that successive discounts cannot simply be added because their bases are different.

Step-by-Step Solution:
Step 1: Marked price (MP) = Rs 1500. Step 2: First discount = 15% of MP = 0.15 * 1500 = Rs 225. Step 3: Price after first discount = 1500 - 225 = Rs 1275. Step 4: Let the second discount rate be d% on Rs 1275. Step 5: Final price after second discount = 1275 * (1 - d/100) = Rs 1173. Step 6: Form the equation 1275 * (1 - d/100) = 1173. Step 7: Divide both sides by 1275 to get 1 - d/100 = 1173 / 1275. Step 8: 1173 / 1275 = 0.92, so 1 - d/100 = 0.92. Step 9: d/100 = 1 - 0.92 = 0.08, so d = 8. Step 10: Therefore, the second discount rate is 8%.

Verification / Alternative check:
We can verify by forward calculation. After the first 15% discount, the price is 1500 * 0.85 = 1275. Applying an 8% discount gives 1275 * 0.92 = 1173. This exactly matches the given final price, confirming that 8% is correct.

Why Other Options Are Wrong:

• 15%: This would give a much lower final price than 1173 because the total effect of two 15% discounts is too large.
• 7%: Using 7% gives a final price of 1275 * 0.93 = 1186.25, not 1173.
• 9%: Using 9% gives a final price of 1275 * 0.91 = 1160.25, which is also incorrect.
• 10%: This would give 1275 * 0.90 = 1147.5, lower than the actual amount paid.

Common Pitfalls:
Many learners assume that the two discounts simply add up and try to guess the second discount from a total discount percentage. Others mistakenly apply the second discount on the original marked price instead of the already reduced price. Errors in forming or solving the equation are also common. Carefully tracking each step and consistently working with the correct base value helps avoid these mistakes.

Final Answer:
The rate of the second discount was 8% on the already reduced price.