Question : A retailer bought 50 kg of Arhar Dal at a discount of 20%. Another 2 kg of Arhar dal was offered to him for free by the wholesaler on the purchase of 50 kg of the dal. If the retailer sells the entire quantity of the dal at the marked price to a customer, what is the profit percentage gained by the retailer?
Option 1: 30%
Option 2: 22%
Option 3: 12%
Option 4: 15%
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Correct Answer: 30%
Solution :
Let the marked price of 1 kg of Arhar Dal as $P$.
The retailer bought 50 kg of Arhar Dal at a discount of 20%.
The cost price for the retailer $= 0.8 × P × 50$
The retailer also received an additional 2 kg of Arhar Dal for free.
The total quantity of Arhar Dal the retailer has = 50 + 2 = 52 kg
If the retailer sells all the Arhar Dal at the marked price.
The selling price $= P × 52$
$\text{Profit percentage} = \frac{\text{Selling price} - \text{Cost price}}{\text{Cost price}} \times 100$
$ =\frac{P \times 52 - 0.8 \times P \times 50}{0.8 \times P \times 50} \times 100$
$ = \frac{12}{40} \times 100$
$= 30\%$
Hence, the correct answer is 30%.
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