The cost price of an article is Rs.480. The marked price of this article is 25% more than its cost price. Two successive discounts of 40% and Rs. X on this article is equal to a single discount of Rs.320. Find the value of X.

### Let's solve this step-by-step.

**1. Marked Price (MP):**  
The marked price is **25% more than the cost price (CP)**.  
Given:  
\[
\text{CP} = 480 \, \text{Rs}
\]
\[
\text{MP} = 480 + (25\% \text{ of } 480)
\]  
\[
\text{MP} = 480 + 120 = 600 \, \text{Rs}
\]

---

**2. Applying successive discounts:**  
1. **First discount:** 40% on the **marked price**.  
   \[
   \text{Price after first discount} = 600 \times \left(1 - \frac{40}{100}\right) = 600 \times 0.6 = 360 \, \text{Rs}
   \]

2. **Second discount:** Rs. \(X\) is subtracted from the price.  
   \[
   \text{Final price after both discounts} = 360 - X
   \]

---

**3. Equivalent single discount of Rs. 320:**  
The **original marked price** was Rs. 600, and after the total discount, the new price becomes \(600 - 320 = 280 \, \text{Rs}\).

---

**4. Equating the final prices:**  
Since both discount methods should result in the same final price:

\[
360 - X = 280
\]

---

**5. Solve for \(X\):**  
\[
X = 360 - 280 = 80
\]

---

### Final Answer:
The value of \(X\) is **80 Rs**.

---

Would you like further clarifications or details?  
Here are five related questions for practice:  

1. If the second discount were \(10\%\) instead of Rs. \(X\), what would the final price be?  
2. How would the answer change if the cost price were Rs. 500?  
3. What would the total percentage discount be after the two successive discounts?  
4. Can you derive a general formula for successive discounts?  
5. What if the first discount were 50%—how would it impact the final price?

**Tip:** Successive discounts are not additive; use the original price at each step for accurate calculations.

This step-by-step solution shows how to solve a problem involving two successive discounts on an article priced at Rs.480. Learn how to calculate the marked price with a 25% increase, apply a 40% discount, and determine the second discount value (Rs. X) to match a single discount of Rs.320. This problem covers core concepts such as percentage, algebra, and successive discounts, suitable for students in Grades 9-12.

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