The marked price of a watch is Rs. 8400. It is sold for Rs. 6896 after two successive discounts. If the first discount is 12%, what is the percentage of the second discount?

Introduction / Context:
This is a successive discount problem that tests understanding of how multiple percentage discounts work on a marked price. Instead of simply adding or subtracting percentages, we must apply each discount step by step on the current price. This is a common type of question in commercial arithmetic and shopkeeper related aptitude problems.

Given Data / Assumptions:

• Marked price (MP) of the watch = Rs. 8400.
• First discount = 12% on the marked price.
• After both discounts, the selling price (SP) becomes Rs. 6896.
• The second discount is applied on the already reduced price after the first discount.
• We must find the second discount percentage.

Concept / Approach:
Successive discounts are applied multiplicatively, not additively. The first discount reduces the marked price to MP * (1 - first discount). The second discount then reduces this new price further to a final selling price. To find the missing second discount, compute the price after the first discount, then set up an equation where that price multiplied by (1 - second discount) equals the final selling price. Solve for the second discount rate and convert it to a percentage.

Step-by-Step Solution:
Step 1: Marked price MP = 8400. Step 2: First discount = 12%, so price after first discount = 8400 * (1 - 0.12) = 8400 * 0.88. Step 3: Compute 8400 * 0.88 = 7392. So, reduced price after the first discount = Rs. 7392. Step 4: Let the second discount be d (expressed as a decimal). Then final selling price SP = 7392 * (1 - d). Step 5: We are given SP = 6896. Set up the equation 7392 * (1 - d) = 6896. Step 6: Divide both sides by 7392: 1 - d = 6896 / 7392. Step 7: 6896 / 7392 is approximately 0.9329. Hence d = 1 - 0.9329 = 0.0671 approximately. Step 8: Convert to percentage: d% = 0.0671 * 100 ≈ 6.71%. The closest option is 6.709%.

Verification / Alternative check:
We can verify by taking the approximate second discount 6.709%. Compute the final selling price again: 7392 * (1 - 0.06709) = 7392 * 0.93291 ≈ 6896. This matches the given selling price, so the computed second discount is correct. Small rounding differences are expected due to decimal approximation, but the option 6.709% fits this calculation very closely.

Why Other Options Are Wrong:
7.2%, 9.14% and 7.13% all give final prices that differ more significantly from Rs. 6896 when applied after the first discount. They either reduce the price too much or not enough. Only 6.709% produces a selling price that agrees with the given value within normal rounding tolerance.

Common Pitfalls:
A frequent error is to treat successive discounts as simply 12% + x% and compare that total to the overall reduction from 8400 to 6896. That approach ignores that each discount is applied on a different base value. Another mistake is to round intermediate values too aggressively, which can push the final percentage away from the correct option. Always apply discounts sequentially and keep at least four decimal places during calculation when multiple percentages are involved.

Final Answer:
The second discount rate is approximately 6.709%.