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A dishonest shopkeeper sells sugar at 40/kg which costs him 45/kg. By using faulty weights, he gives 800 gm instead of 1 kg. What is his total percentage profit or loss?
11.11% profit
11.11% loss
12.5% profit
12.5% loss
11.11% profit
Given: Cost price of 1 kg is 45. Selling price of 1 kg is 40. The shopkeeper gives 800 gm instead of 1000 gm.
Cost price of 1 kg is 45. Selling price of 1 kg is 40. The shopkeeper gives 800 gm instead of 1000 gm.
Profit/Loss┬аPercentage=(Cost┬аPriceSelling┬аPriceтАЛтИТ1)├Ч100%
Use the ratio: (CPSPтАЛ├ЧQuantity┬аBoughtQuantity┬аSoldтАЛ). Here: (4540тАЛ├Ч8001000тАЛ)=(98тАЛ├Ч45тАЛ)=910тАЛ. Profit is (910тАЛтИТ1)=1/9, which is 11.11%.
Students often try to calculate the loss on price and the profit on weight separately, forgetting that the actual cost price for the 800 gm given is 0.8├Ч45=36.
Calculate the Cost Price for 800 gm
Since the cost price of 1 kg (1000 gm) is 45, the cost price of 800 gm is 0.8├Ч45=36.
CPactualтАЛ=100045тАЛ├Ч800=36
Identify the Actual Selling Price
The shopkeeper sells what he labels as 1 kg for 40, but he only gives 800 gm. Thus, he receives 40 for 800 gm.
SP=40
Calculate Profit Percentage
Profit is SPтИТCP=40тИТ36=4. Percentage profit is 364тАЛ├Ч100%.
Profit%=3640тИТ36тАЛ├Ч100%=91тАЛ├Ч100%=11.11%
A is correct because the net profit calculation 3640тИТ36тАЛ├Ч100% results in 11.11% profit.
This concept is similar to 'Successive Percentage Changes' in Compound Interest and Data Interpretation problems involving quantities and rates.