Marked price of A is Rs. 1600 more than its cost price. When discount on A is 500, a profit of 25\% is obtained. At what price should A be sold to obtain a 30\% profit?

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Accepted Answer

**Solution:**

1. Let the cost price be $ CP $.
2. Marked price $ MP = CP + 1600 $  (Given)

3. When discount is 500, profit is 25%:
   - Selling price $ SP = MP - 500 = CP + 1600 - 500 = CP + 1100 $
   - Profit = 25% means:
     $$
     SP = CP + 0.25 \times CP = 1.25 CP
     $$

4. Equate the two expressions for $ SP $:
   $$
   CP + 1100 = 1.25 CP \ 
   1100 = 1.25 CP - CP = 0.25 CP \ 
   CP = \frac{1100}{0.25} = 4400
   $$

5. Now, to get 30% profit, selling price should be:
   $$
   SP = CP + 0.30 \times CP = 1.30 \times 4400 = 5720
   $$

**Answer:** Rs. $ 5720 $ (None of the given options)

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