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A dishonest shopkeeper professes to sell his goods at cost price. However, he uses a false weight and thus gains 25%. For a kg, he uses a weight of:
850 gm
800 gm
700 gm
900 gm
800 gm
Use the ratio of 100:(100+gain%) for weights: 1000:1250 reduces to 4:5. The false weight is the smaller part: (4/5)├Ч1000=800 gm.
Profit percentage = 25%, standard weight = 1000 gm, selling at cost price.
Gain%=(False┬аweightTrue┬аweightтИТFalse┬аweightтАЛ)├Ч100
Use the ratio of 100:(100+gain%) for weights: 1000:1250 reduces to 4:5. The false weight is the smaller part: (4/5)├Ч1000=800 gm.
Confusing the gain percentage relative to the cost price with the gain percentage relative to the false weight used; gain is actually calculated on the weight actually given, not the weight promised.
Define the relationship
Let the actual weight sold be x. Since the shopkeeper sells at cost price, the gain comes from the difference between the actual weight (1000 gm) and the false weight x. The profit percentage is given by:
25=(x1000тИТxтАЛ)├Ч100
Solve for x
Simplify the equation: divide by 100 to get 0.25=x1000тИТxтАЛ. Multiply by x: 0.25x=1000тИТx. Combine terms: 1.25x=1000.
x=1.251000тАЛ=800
Conclusion
The value of x is 800, which represents the false weight used by the shopkeeper.
x=800┬аgm
B is correct because the calculation x=1.251000тАЛ=800 results in 800 gm.
This is equivalent to problems involving 'false scales' where you replace the standard formula costprofitтАЛ with false┬аweighterrorтАЛ.
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