Let the marked price of the article be Rs. 4000. The customer buys the article after two successive discounts of $x\%$ each, and the final price paid is Rs. 3610.

Step-by-step solution:

1. First Discount Application: After the first discount of $x\%$, the price becomes: $\text{Price after 1st discount} = 4000 \times \left(1 - \frac{x}{100}\right)$

2. Second Discount Application: After the second discount of $x\%$ on the new price, the final price becomes: $\text{Final price} = 4000 \times \left(1 - \frac{x}{100}\right) \times \left(1 - \frac{x}{100}\right) = 3610$ Simplifying: $4000 \times \left(1 - \frac{x}{100}\right)^2 = 3610$ Dividing both sides by 4000: $\left(1 - \frac{x}{100}\right)^2 = \frac{3610}{4000}$ $\left(1 - \frac{x}{100}\right)^2 = 0.9025$

3. Solving for $x$: Taking the square root on both sides: $1 - \frac{x}{100} = \sqrt{0.9025}$ $1 - \frac{x}{100} = 0.95$ Solving for $x$: $\frac{x}{100} = 1 - 0.95 = 0.05$ $x = 5$

Thus, the value of $x$ is 5%. The correct answer is (D) 5%.

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Related Questions:

1. What would be the final price if the successive discounts were 10% each?
2. How does the formula for successive discounts work in general cases?
3. What is the impact of a single discount of $2x\%$ compared to two successive discounts of $x\%$?
4. How would the calculation change if the final price was Rs. 3500 instead of Rs. 3610?
5. How does compound interest compare with successive discounts?

Tip: Successive percentage discounts compound multiplicatively, not additively.