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A merchant buys a product at 15% discount on the Selling price. He receives an additional discount of 20% on the new selling price. The merchant sold this product in his local market and incurs a loss of 10% which comes out to be Rs. 2000. What was the approximate initial selling price offered to the merchant?

A merchant buys a product at 15% discount on the Selling price. He receives an additional discount of 20% on the new selling price. The merchant sold this product in his local market and incurs a loss of 10% which comes out to be Rs. 2000. What was the approximate initial selling price offered to the merchant? Correct Answer 29412

Let Merchant’s Cost Price = MCP

Merchant’s Selling price = MSP

(MSP - MCP)/(MCP) = 0.1

MSP = 1.1 MCP

LOSS = Rs. 2000

This means MCP – MSP = Loss = 2000

0.1 MCP = Rs. 2000

MCP = Rs. 20000

Hence the merchant bought the product at Rs. 20000

Let the cost price of the product before the second discount of 20% is X

X - 0.2X = Rs. 20000

⇒ X = 20000/0.8

⇒ X = Rs.25000

Let the price of the product before the first discount that is the initial price be Y

Y - 0.15Y = 25000

⇒ Y = 25000/0.85 = Rs 29411.76 = Rs 29412

SHORT TRICK:

Let the Selling price be = Rs.100 unit 

⇒ After 15% discount, CP = Rs. 85 unit

⇒ Another discount of 20% is given

⇒ Successive discount = 15 + 20 – (15 × 20)/100 = 32%

⇒ After 32% discount, CP = Rs. 68 unit

⇒ Loss = 10% on CP = 10% of 68 = Rs.6.8 unit

Given that 6.8 unit loss = Rs. 2000

∴ Selling Price = (2000/6.8) × 100 unit ≈  Rs. 29412

 

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