After two successive discount each of x% on
marked price of an article, a customer buy it for
Rs. 3610. If marked price of the article is Rs. 4000. Find value of x. (A) 25% (B) 15% (C) 10% (D) 5%

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%.

Would you like further details or have any questions?

### 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.

After two successive discount each of x% on marked price of an article, a customer buy it for Rs. 3610. If marked price of the article is Rs. 4000. Find value of x. (A) 25% (B) 15% (C) 10% (D) 5%

This problem involves finding the successive discount percentage on a marked price of Rs. 4000, where the final price paid is Rs. 3610. Learn how to apply successive percentage discount formulas and solve for the unknown discount rate. Suitable for students in Grades 8-10.

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