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
By selling a watch at Rs. 840 a person loses 4%. Find the gain or loss if he sold it for Rs. 875?
Gaurav bought some articles at 5 for Rs. 6 and sold them at 10 for Rs. 11. His loss percentage is:
The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?
- The selling price of 24 articles is equal to the cost price of 26 articles. If, due to a change in market conditions, the selling price of each article decreases by $10\%$ and the cost price of each article increases by $5\%$, what will be the new gain or loss percentage (correct to two decimal places)?
Anil bought some articles at 6 for Rs. 8 and sold them at 10 for Rs. 12. His percentage loss or gain is:
