A watch with marked price 8,400 rupees is sold for 5,040 rupees after two successive discounts. If the first discount is 25 percent, what is the percentage of the second discount?

Introduction / Context:
This question involves successive discounts and requires finding the second discount rate when the combined effect of two discounts is known. Successive discounts are common in retail pricing and exam problems, and understanding that they are multiplicative rather than additive is essential.

Given Data / Assumptions:
- Marked price (MP) of the watch = 8,400 rupees.
- First discount = 25 percent.
- Final selling price (SP) after two discounts = 5,040 rupees.
- Let the second discount rate be x (expressed as a decimal, for example 0.2 for 20 percent).
- We must find x, and then express it as a percentage to match the answer options (noting that the options here are given as decimals representing the fraction, not the percent symbol itself).

Concept / Approach:
A 25 percent discount on the marked price means the price becomes 75 percent of the marked price, or 0.75 * MP. Then the second discount of rate x is applied on this reduced price, so the customer finally pays (1 - x) of that reduced amount. Thus, SP = MP * 0.75 * (1 - x). Knowing SP and MP, we can solve for x.

Step-by-Step Solution:
Step 1: After a 25 percent discount, the price becomes 75 percent of 8,400 rupees.Step 2: Compute 75 percent of 8,400: 0.75 * 8,400 = 6,300 rupees.Step 3: Let the second discount rate be x, so after the second discount the buyer pays (1 - x) of 6,300.Step 4: Final selling price SP = 6,300 * (1 - x) = 5,040 rupees.Step 5: Form the equation: 6,300 * (1 - x) = 5,040.Step 6: Divide both sides by 6,300: 1 - x = 5,040 / 6,300.Step 7: Simplify 5,040 / 6,300 = 0.8.Step 8: So 1 - x = 0.8, which gives x = 1 - 0.8 = 0.2.

Verification / Alternative check:
If the second discount is 0.2, that is 20 percent, then after first reducing the price to 6,300 rupees, a further 20 percent discount is 0.20 * 6,300 = 1,260 rupees. Subtracting 1,260 from 6,300 gives 5,040 rupees, which matches the given final selling price. This confirms that the second discount rate is 0.2 (20 percent).

Why Other Options Are Wrong:
- 0.15 (15 percent) and 0.25 (25 percent) would produce different final prices when applied on 6,300 rupees.
- 0.3 (30 percent) would reduce the price too much and produce a selling price lower than 5,040 rupees.

Common Pitfalls:
A common error is to simply add the two discounts as 25 percent plus x and try to match combined percentage directly with SP and MP. However, successive discounts are not additive; they are applied one after another, leading to a multiplicative combined factor. Always express each discount as a factor on the price in sequence and then solve using the given final selling price.

Final Answer:
The second discount rate is 0.2, which corresponds to 20 percent.