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A trader claims to sell flour at a profit of 35%, but also dishonestly uses a weight which is 16% 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.)
56%
63%
60%
61%
61%
Use the formula: 100тИТyx+yтАЛ├Ч100, where x is the declared profit % and y is the % of weight error. Here, 100тИТ1635+16тАЛ├Ч100=8451тАЛ├Ч100=60.71%.
Profit margin on cost = 35%, Error in weight = 16% less than true weight.
Total┬аProfit┬аPercentage=(100тИТError┬аPercentageProfit┬аPercentage+Error┬аPercentageтАЛ)├Ч100
Use the formula: 100тИТyx+yтАЛ├Ч100, where x is the declared profit % and y is the % of weight error. Here, 100тИТ1635+16тАЛ├Ч100=8451тАЛ├Ч100=60.71%.
Students often calculate profit as 35%+16%=51%, failing to account for the reduction in the cost basis due to the dishonest weight.
Define Cost and Revenue
Assume the cost price of 100g is 100. The trader marks up by 35%, so the selling price for what he claims is 100g is $135.
SP=135,CP=100
Account for Dishonest Weight
The trader actually gives 16% less than 100g, which is 84g. The cost price of 84g is $84.
Actual┬аCP=84
Calculate Final Profit Percentage
Profit = 135тИТ84=51. Profit percentage = (51/84)├Ч100.
8451тАЛ├Ч100=60.714...%тЙИ61%
D is correct because the effective profit percentage is calculated as 60.71%, which rounds to 61%.
This concept is a variation of 'Successive Percentage Change' where one change is on the price and the other is on the quantity; always ensure you find the effective CP after the quantity reduction.
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