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A merchant sells two items for 24000 rupees each. He gets a profit of 20% on one item and loses 20% on the other. What is his overall profit or loss percentage?
4% loss
4% profit
2% loss
No profit, no loss
4% loss
Whenever the selling price of two items is the same and the profit and loss percentages are equal, the overall transaction always results in a loss given by the square of the rate divided by 100.
Selling Price of each item = 24000 rupees, Profit on one item = 20%, Loss on the other = 20%.
Loss%=(100x2тАЛ)%
Whenever the selling price of two items is the same and the profit and loss percentages are equal, the overall transaction always results in a loss given by the square of the rate divided by 100.
Students often assume that 20% profit and 20% loss cancel each other out to result in 0% net change (No profit, no loss).
Identify the scenario
Since the items are sold at the same price and the profit/loss percentages are numerically equal, we apply the net percentage change formula.
Net┬аeffect=(x+y+100xyтАЛ)%
Substitute the values
Here, x=+20 (profit) and y=тИТ20 (loss). Substituting these into the formula:
20тИТ20+10020├Ч(тИТ20)тАЛ
Calculate the result
The terms 20 and тИТ20 cancel out, leaving the remainder of the calculation:
100тИТ400тАЛ=тИТ4%
Conclusion
The negative sign indicates a loss of 4%.
4%┬аLoss
A is correct because when selling prices are equal and profit/loss percentages are identical, the result is always a loss calculated as x2/100, which is 202/100=4%.
This concept of equal percentage gain and loss resulting in a net loss is identical to the 'Successive Percentage Increase/Decrease' concept used in compound interest and population growth problems.
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