Calculating Shopkeeper's Total Gain Percentage
The problem involves calculating the total percentage gain when a shopkeeper uses tampered weights to cheat by 8% during both buying and selling.
We can treat the cheating in buying and selling as two separate instances of percentage gain applied sequentially.
Gain from Cheating in Buying
When buying, the shopkeeper cheats by 8%. This means he gets 8% more quantity than he pays for. This effectively results in a gain of 8%.
Buying Gain = $8\%$
Gain from Cheating in Selling
When selling, the shopkeeper cheats by 8%. This means he gives 8% less quantity than the customer pays for. This effectively results in a gain of 8% on the selling price.
Selling Gain = $8\%$
Calculating Total Gain Percentage
To find the total gain percentage when two successive percentage gains (or losses) occur, we use the formula:
$ \text{Total Gain \%} = x + y + \frac{xy}{100} $
Where $x$ is the first gain percentage and $y$ is the second gain percentage.
In this case, $x = 8\%$ and $y = 8\%$.
$ \text{Total Gain \%} = 8 + 8 + \frac{8 \times 8}{100} $
$ \text{Total Gain \%} = 16 + \frac{64}{100} $
$ \text{Total Gain \%} = 16 + 0.64 $
$ \text{Total Gain \%} = 16.64\% $
Conclusion
The shopkeeper's total gain percentage is 16.64%.
Similar Questions
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Important Questions from Successive Selling
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A single discount equivalent to three successive discounts i.e. 7%, 12% and 5% is:
Two successive discounts, with the first being 10%, were given on an article having the marked price of ₹ 7,500. Finally, it was sold for ₹ 5,805. What percent was the second discount ?
The marked price of an article is ₹450. It is sold for ₹267.30, after offering three successive discounts of 10%, x%, and 20%. What is the value of x?
