A retailer marks an article at 35\% above its cost price and gains Rs 96 by offering a 20\% discount on the marked price. If the retailer instead gives a 15\% discount on the marked price, what is the profit earned on selling one article?

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Accepted Answer

**Solution:**

1. Let the cost price of the article be $100x$.

2. The marked price is 35\% above cost price, so:
   $$\text{Marked Price} = 100x \times \frac{135}{100} = 135x$$

3. Given that by giving a 20\% discount on the marked price, the retailer earns Rs 96 profit:
   $$
   135x \times \frac{80}{100} - 100x = 96
   $$
   Simplifying:
   $$
   108x - 100x = 96 \ 
   8x = 96 \ 
   x = \frac{96}{8} = 12
   $$

4. Now, if the retailer gives a 15\% discount on the marked price, the selling price becomes:
   $$135x \times \frac{85}{100} = 114.75x$$

5. Profit in this case:
   $$
   114.75x - 100x = 14.75x
   $$
   Substitute $x = 12$:
   $$
   14.75 \times 12 = 177
   $$

**Answer:** Rs 177

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