The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is

Question

Accepted Answer

The problem involves calculating the original selling price of a product based on profit percentages and changes in cost price and selling price. Here's the step-by-step solution:

**Define Variables:**

- Let the original cost price (CP) of the product be $$x$$.
   - The selling price (SP) is fixed to ensure a 40% profit:
     $$
     SP = 1.4x
     $$

**New Scenario:**

- The new cost price is 40% less than the original cost price:
     $$
     	ext{New CP} = 0.6x
     $$
   - The new selling price is $$5$$ rupees less than the original selling price:
     $$
     	ext{New SP} = 1.4x - 5
     $$
   - The profit percentage in this scenario is 50%, so:
     $$
     	ext{New SP} = 	ext{New CP} 	imes (1 + 0.5)
     $$

**Set Up the Equation:**

Substitute values into the profit equation:
   $$
   1.4x - 5 = 0.6x 	imes 1.5
   $$
   Simplify:
   $$
   1.4x - 5 = 0.9x
   $$
   Rearrange terms:
   $$
   0.5x = 5
   $$
   Solve for $$x$$:
   $$
   x = 10
   $$

**Calculate Original Selling Price:**

Using the formula for SP:
   $$
   SP = 1.4x = 1.4 	imes 10 = 14
   $$

### Final Answer:
The original selling price of the product is **14 rupees**.  
Correct option: **D**

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