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.

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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!