In order to convert a loss of 5% to a profit of 5%, a shopkeeper raise

In order to convert a loss of 5% to a profit of 5%, a shopkeeper raises the price of an item by ₹ 500. What is the cost price of the item ?

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₹ 1,000

₹ 5,000

₹ 10,000

₹ 1,200

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC CISF-AC-EXE – 2022

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Let the cost price (CP) of the item be ₹ x. Initially, the shopkeeper incurs a loss of 5%. The selling price (SP1) in this case is CP – 5% of CP = x – 0.05x = 0.95x. To convert this to a profit of 5%, the new selling price (SP2) must be CP + 5% of CP = x + 0.05x = 1.05x.

The problem states that the shopkeeper raises the price of the item by ₹ 500 to achieve the desired change. This means the difference between the new selling price (SP2) and the original selling price (SP1) is ₹ 500.
SP2 – SP1 = ₹ 500.
(1.05x) – (0.95x) = 500.

Subtracting the two expressions for the selling prices in terms of CP (x):
(1.05 – 0.95) * x = 500.
0.10 * x = 500.
To find x (the cost price), divide 500 by 0.10:
x = 500 / 0.10 = 500 / (1/10) = 500 * 10 = ₹ 5,000.
The price increase of ₹ 500 represents the change from a 5% loss margin to a 5% profit margin, which is a total change of 10% of the cost price (5% below CP to 5% above CP). So, 10% of CP = 500, which directly leads to CP = 5000.

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