Computer Sciences > GATE 2024 SET-2 > Profit and Loss
A person sold two different items at the same price. He made 10% profit in one item, and 10% loss in the other item. In selling these two items, the person made a total of
Correct : c
Let the Selling Price (SP) of each item = ₹100
For Item 1 (10% Profit):
SP = CP × (100 + Profit%) ÷ 100
100 = CP × 110 ÷ 100
CP = 100 × 100 ÷ 110
CP1 = ₹90.91
For Item 2 (10% Loss):
SP = CP × (100 − Loss%) ÷ 100
100 = CP × 90 ÷ 100
CP = 100 × 100 ÷ 90
CP2 = ₹111.11
Total SP = 100 + 100 = ₹200
Total CP = 90.91 + 111.11 = ₹202.02
Since Total CP > Total SP, there is a Loss
Net Loss = 202.02 − 200 = ₹2.02
Loss% = (Net Loss ÷ Total CP) × 100
Loss% = (2.02 ÷ 202.02) × 100
Loss% = 1%
Shortcut Formula:
Net Loss% = (Common%)2 ÷ 100
Net Loss% = (10)2 ÷ 100
Net Loss% = 100 ÷ 100
Net Loss% = 1%
The person made a net loss of 1%
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