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A man sells two houses at the rate of ₹1.995 lakhs each. On one he gains 5% and on the other he loses 5%. His gain or loss percentage in the whole transaction is:
0.25% loss
0.25% gain
25% loss
5% loss
0.25% loss
When the selling price of two items is the same and one is sold at a profit of x% and the other at a loss of x%, the total transaction always results in a loss of 100x2%.
Selling price of each house is ₹1.995 lakhs. Profit percentage on first house is 5%. Loss percentage on second house is 5%.
Loss%=(100x2)%
When the selling price of two items is the same and one is sold at a profit of x% and the other at a loss of x%, the total transaction always results in a loss of 100x2%.
Many students try to calculate the exact monetary profit and loss and add them, which is unnecessary and time-consuming; the total selling price value (1.995 lakhs) is irrelevant for finding the percentage.
Identify the conditions
The problem states two items are sold for the same price, with an equal percentage gain and loss (x=5).
x=5
Apply the direct formula
Since the selling prices are equal and the gain/loss percentages are equal, the net result is always a loss.
Loss%=(100x2)%=(10052)%
Calculate the result
Calculate the value by squaring 5 and dividing by 100.
Loss%=10025=0.25%
A is correct because when two items are sold at the same price with an equal percentage gain and loss, the overall transaction always results in a loss of 100x2%, which equals 0.25%.
This concept is a classic in competitive exams; always check if selling prices are equal before applying the 100x2 shortcut.
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