a dishonest shopkeeper has two false balances. one balance weighs 10% more while buying the goods and other weighs 10% less while selling the goods. find his gain percent just by weighing
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Answers
Step-by-step explanation:
Cheats to the extent of 10%" is ambiguous. It can either mean that the error is 10% of the true weight of the goods, or that the error is 10% of weight that the shopkeeper pays/charges for.
These two interpretations lead to different results.
Suppose that he buys and sells one kilogram of goods at a market price of $1000 per kilogram.
Under the first interpretation he would pay his supplier for 900 grams of goods but charge his customer for 1100 grams, making a profit of $200.
Under the second interpretation he would pay his supplier for (approximately) 909 grams of goods and charge his customer for 1111 grams, making a profit of $202.
An additional ambiguity creeps in when we try to express the profits $200 and $202 as percentages of something -- percentages of what? The merchant's initial outlay? The true value of the kilogram of goods? The retail price? Each of those choices, too, yield different answers.
Thus I think at least the following answers could all be justified:
2001000=20%200900=22.2%2021000=20.2%202909=22.2%
We would get 21% by saying that the shopkeeper earns a profit of 10% when buying and again when selling -- and 1.10×1.10=1.21 -- but the total profit in dollars doesn't appear to be 21% of any relevant amount that could possibly arise during the transaction.
In order to get 21% we would need to say that "cheats to extent of 10%" means that the error in the shopkeeper's measurements is 10% of the lower of the true weight and what the shopkeeper says the weight is. Then he would buy for $909 and sell for $1100. But that would be a very artificial and unlikely interpretation of "cheating by 10%".
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