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A trader claims to sell spice at a profit of 15% but also dishonestly uses a weight which is 14% less than what is mentioned on it. Find the total percentage of profit earned by the trader. (Round the answer to the nearest whole number) 1691
31%
36%
34%
39%
34%
Assume CP of 1000g = 1000 units. Sell at 15% profit (1150) but give 14% less weight (860g). Gain = (1150-860)/860 = 290/860.
Reported profit percentage = 15%, Dishonest weight usage = 14% less than actual.
Profit%=(CPSPтАЛтИТ1)├Ч100
Assume CP of 1000g = 1000 units. Sell at 15% profit (1150) but give 14% less weight (860g). Gain = (1150-860)/860 = 290/860.
Students often add 15% and 14% to get 29%, which ignores the denominator change in profit calculation.
Define base values
Assume the cost price of 1000g of spice is 1000 units. The trader marks up the price by 15%, so the selling price for 1000g is 1150 units.
CP=1000,SP=1150
Calculate effective weight
The trader uses a weight 14% less than 1000g. Thus, the actual weight delivered is 860g.
Weight=1000тИТ(0.14├Ч1000)=860
Calculate actual profit
The actual cost to the trader for 860g is 860 units. He sells this amount for 1150 units.
Profit=1150тИТ860=290
Find profit percentage
Profit percentage is calculated on the actual cost price (860).
Profit%=(860290тАЛ)├Ч100тЙИ33.72%
C is correct because the calculated profit percentage is approximately 33.72%, which rounds to 34%.
This concept of 'error in measurement' is identical to error analysis in physics experiments, where percentage error is x╬ФxтАЛ├Ч100.
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