**Given:**

- Cost price of a product = Rs $Y$
- Marked price = 60\% above cost price
- Retailer offers 25\% discount on marked price
- Retailer earns a profit of Rs 40

**Quantities:**

- Quantity I: Find the marked price of the product (in Rs).
- Quantity II: If the cost price of an article equals the selling price of the product, and the article is sold at 33.33\% profit, find the selling price of the article.

**Compare Quantity I and Quantity II:**

Question

**Given:**

- Cost price of a product = Rs $Y$
- Marked price = 60\% above cost price
- Retailer offers 25\% discount on marked price
- Retailer earns a profit of Rs 40

**Quantities:**

- Quantity I: Find the marked price of the product (in Rs).
- Quantity II: If the cost price of an article equals the selling price of the product, and the article is sold at 33.33\% profit, find the selling price of the article.

**Compare Quantity I and Quantity II:**

Accepted Answer

**Solution:**

1. Let the cost price (CP) of the product be Rs $Y$.

2. Marked price (MP) is 60\% above CP:
   $$MP = Y + 0.6Y = 1.6Y$$

3. Retailer gives 25\% discount on MP, so selling price (SP) is:
   $$SP = MP \times (1 - 0.25) = 1.6Y \times 0.75 = 1.2Y$$

4. Retailer earns a profit of Rs 40, so:
   $$SP - CP = 40 \implies 1.2Y - Y = 40 \implies 0.2Y = 40 \implies Y = \frac{40}{0.2} = 200$$

5. Now, find Quantity I (MP):
   $$MP = 1.6Y = 1.6 \times 200 = 320$$

6. For Quantity II:
   - Cost price of article = SP of product = Rs 1.2Y = Rs 240
   - Article sold at 33.33\% profit means profit = $\frac{1}{3}$ of cost price.

7. Selling price of article:
   $$SP_{article} = CP_{article} + Profit = 240 + \frac{1}{3} \times 240 = 240 + 80 = 320$$

8. Compare Quantity I and Quantity II:
   - Quantity I = 320
   - Quantity II = 320

Since both quantities are equal, the correct answer is option (e).

**Answer:** (e) Quantity I = Quantity II or no relation

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