A seller marks the price of an item 50\% above the cost price and offers a 10\% discount to the customer. However, he cheats by giving 20\% less weight than the actual quantity. What is the approximate overall profit percentage of the seller?

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Accepted Answer

**Solution:**

1. Let the cost price (CP) of the item be $100$ units.

2. The seller marks the price 50\% above the cost price, so the marked price (MP) is:
   $$
   MP = 100 + 50\% \times 100 = 150
   $$

3. The seller gives a 10\% discount on the marked price, so the selling price (SP) per actual weight is:
   $$
   SP = 150 - 10\% \times 150 = 150 - 15 = 135
   $$

4. However, the seller cheats by giving 20\% less weight. This means the customer receives only 80\% of the actual quantity but pays for the full quantity.

5. Therefore, the effective selling price for the actual cost price is:
   $$
   \text{Effective SP} = \frac{135}{0.8} = 168.75
   $$

6. The profit is the difference between the effective selling price and the cost price:
   $$
   \text{Profit} = 168.75 - 100 = 68.75
   $$

7. The profit percentage is:
   $$
   \text{Profit \%} = \frac{68.75}{100} \times 100 = 68.75\% \approx 65\% \text{ (closest option)}
   $$

**Answer:** 65\%

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