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Question

A shopkeeper buys shirts from a producer and sells them at 20% profit. A customer has to pay ₹3,186.00 including 18% taxes, per shirt. At what price did the shopkeeper buy each shirt from the producer?

The correct answer is
₹2,250.00

The problem asks for the price at which the shopkeeper bought the shirts from the producer. We are given the final price paid by the customer, the tax rate, and the shopkeeper's profit percentage.

Calculate Selling Price Before Tax

The customer pays ₹3,186.00, which includes an 18% tax. Let the selling price before tax be denoted by $SP_{no\_tax}$.

The final price is calculated as: $SP_{no\_tax} \times (1 + \text{Tax Rate})$

Therefore, $SP_{no\_tax} \times (1 + 0.18) = 3186.00$

$SP_{no\_tax} \times 1.18 = 3186.00$

To find the selling price before tax:

$SP_{no\_tax} = \frac{3186.00}{1.18} = 2700.00$

So, the shopkeeper's selling price (before tax) was ₹2,700.00.

Determine Purchase Price

The shopkeeper sells the shirts at a 20% profit. This means the selling price ($SP_{no\_tax}$) is 20% higher than the purchase price ($CP$).

The relationship is: $CP \times (1 + \text{Profit Rate}) = SP_{no\_tax}$

$CP \times (1 + 0.20) = 2700.00$

$CP \times 1.20 = 2700.00$

To find the purchase price:

$CP = \frac{2700.00}{1.20} = 2250.00$

The shopkeeper bought each shirt from the producer for ₹2,250.00.

Final Answer Summary

  • Selling Price including 18% tax = ₹3,186.00
  • Selling Price before tax = ₹2,700.00
  • Shopkeeper's Profit = 20%
  • Shopkeeper's Purchase Price = ₹2,250.00
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Important Questions from Profit and Loss

  1. By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?

  2. By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?

  3. The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?

  4. The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?

  5. A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?

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