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A man sells two chairs for Rs 600 each. On one he gains 20% and on the other he loses 20%. What is his overall gain or loss percentage?
4%┬аloss
4%┬аgain
No┬аprofit┬аno┬аloss
2%┬аloss
4%┬аloss
Whenever two items are sold at the same price with the same profit and loss percentage (x%), there is always an overall loss given by x2/100.
Selling Price of each chair = Rs 600. Profit percent on first chair = 20%. Loss percent on second chair = 20%.
Loss%=(100x2тАЛ)%
Whenever two items are sold at the same price with the same profit and loss percentage (x%), there is always an overall loss given by x2/100.
Many students wrongly assume the net result is 'No profit no loss' because the percentage values (20% and -20%) cancel each other out, ignoring that these percentages are calculated on different base costs.
Identify the scenario
Since the selling prices are equal and the percentage of gain and loss are identical, we use the standard shortcut for equal percentage gain and loss.
Gain=20%,Loss=20%,SP1тАЛ=SP2тАЛ=600
Apply the formula
The overall loss percentage is calculated using the formula x2/100, where x=20.
Loss%=100202тАЛ=100400тАЛ
Calculate the result
Dividing 400 by 100 gives a loss of 4%.
Loss=4%
A is correct because when an item is sold at a gain of x% and another at a loss of x%, the net result is always a loss of (x┬▓/100)%, which calculates to 4%.
This shortcut is a specific case of the 'Successive Percentage Change' concept (A + B + AB/100), where A = 20 and B = -20.
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