The present selling price of Article A after allowing a discount of 15% on its cost price, is the same as the present selling price of Article B after allowing a discount of 25% on its cost price. Earlier Ramesh had purchased 34 pieces of Article A and 32 pieces of Article B at 10% discount on its cost price for Rs. 33,480. What is the present selling price (in Rs.) of each article?

Let's define the variables for the problem:

- Let the **cost price** of Article A be \( C_A \).
- Let the **cost price** of Article B be \( C_B \).

### Step 1: Relationship between selling prices
The selling price of Article A after a 15% discount on its cost price is:
\[
S_A = C_A - 0.15C_A = 0.85C_A
\]

Similarly, the selling price of Article B after a 25% discount on its cost price is:
\[
S_B = C_B - 0.25C_B = 0.75C_B
\]

It is given that the selling prices of Articles A and B are the same, so:
\[
0.85C_A = 0.75C_B
\]
From this equation, we can express \( C_B \) in terms of \( C_A \):
\[
C_B = \frac{0.85}{0.75}C_A = \frac{17}{15}C_A
\]

### Step 2: Cost of purchasing articles
Ramesh purchased 34 pieces of Article A and 32 pieces of Article B at a 10% discount on their cost prices. So the total cost paid by Ramesh is:
\[
\text{Total cost} = 34 \times 0.9C_A + 32 \times 0.9C_B = 33,480
\]
Substituting \( C_B = \frac{17}{15}C_A \) into this equation:
\[
34 \times 0.9C_A + 32 \times 0.9 \times \frac{17}{15}C_A = 33,480
\]
Simplifying this equation:
\[
30.6C_A + 32 \times 0.9 \times \frac{17}{15}C_A = 33,480
\]
\[
30.6C_A + 32 \times 1.02C_A = 33,480
\]
\[
30.6C_A + 32.64C_A = 33,480
\]
\[
63.24C_A = 33,480
\]
\[
C_A = \frac{33,480}{63.24} = 529.35
\]

### Step 3: Calculate \( C_B \)
Now that we know \( C_A \), we can find \( C_B \):
\[
C_B = \frac{17}{15} \times 529.35 = 599.26
\]

### Step 4: Calculate present selling prices
The present selling price of Article A is:
\[
S_A = 0.85 \times 529.35 = 449.95
\]

The present selling price of Article B is:
\[
S_B = 0.75 \times 599.26 = 449.45
\]

So, the present selling price of each article is approximately Rs. **450**.

---

Would you like any further clarifications or details on this? 

Here are 5 related questions you might find interesting:
1. What would the selling price be if the discount for Article A was 20% instead of 15%?
2. How much profit or loss did Ramesh make if he sold all articles at their present selling prices?
3. What is the break-even price for both articles assuming no discount?
4. If Ramesh had purchased more articles at a different discount rate, how would the overall cost change?
5. How would the relationship between cost prices change if Article B had a different percentage discount?

**Tip:** Always double-check the interpretation of discounts, especially when solving cost and selling price problems involving multiple articles!

This problem involves calculating the present selling prices of two articles after applying discounts of 15% and 25%, respectively. It also includes a step-by-step method of determining cost prices based on the total amount paid and discounts. Suitable for students in Grades 10-12.

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