A shopkeeper cheats to the extent of $10\%$ while buying as well as while selling. While he was eventually caught and punished, at what percent was he gaining till then?
$21\%$
Shopkeeper Gain Calculation
This problem requires calculating the total percentage gain made by a shopkeeper who employs cheating tactics both when buying goods and when selling them.
Analyzing Cheating Percentages
The shopkeeper cheats by $10\%$ while buying and by $10\%$ while selling.
Gain on Buying
When cheating on buying, the shopkeeper effectively gets more value for the money spent. If he spends $₹100$, he receives goods worth $₹100 \times (1 + \frac{10}{100}) = ₹110$. This implies his effective cost price is lower relative to the value received.
Gain on Selling
When cheating on selling, the shopkeeper increases his revenue. If he sells goods worth $₹110$ (the value he acquired), he charges the price for $₹110 \times (1 + \frac{10}{100}) = ₹121$. This means his selling price is higher than the value of goods delivered.
Calculating Net Profit Percentage
To determine the overall gain, let's assume the shopkeeper starts with an initial investment.
- Let the initial amount spent (Cost Price, $CP$) be $₹100$.
- Due to the $10\%$ cheating on buying, the value of goods obtained for $₹100$ is $₹110$.
- The shopkeeper then sells these goods. Due to the $10\%$ cheating on selling, the revenue generated from selling $₹110$ worth of goods is $₹110 \times (1 + \frac{10}{100}) = ₹121$. This is the Selling Price ($SP$).
- The total profit is the difference between the Selling Price and the initial Cost Price:
$ \text{Profit} = SP - CP = ₹121 - ₹100 = ₹21 $
- The profit percentage is calculated with respect to the initial Cost Price ($CP$):
$ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 $
$ \text{Profit Percentage} = \left( \frac{₹21}{₹100} \right) \times 100 = 21\% $
Formula Method for Net Gain
A direct formula can be used for successive percentage gains:
$ \text{Net Gain \%} = \left( x + y + \frac{xy}{100} \right) \% $
Here, $x$ represents the percentage gain on buying ($10\%$) and $y$ represents the percentage gain on selling ($10\%$).
Substituting the values:
$ \text{Net Gain \%} = \left( 10 + 10 + \frac{10 \times 10}{100} \right) \% $
$ \text{Net Gain \%} = \left( 20 + \frac{100}{100} \right) \% = (20 + 1) \% = 21\% $
Thus, the shopkeeper was gaining at a total rate of 21%.
Similar Questions
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Important Questions from Dishonest Dealings
- A trader claims to sell pulses at a profit of 3%, but also dishonestly uses a weight which is 15% less than what is mentioned on it. Find the total percentage of profit earned by the trader. (Round off the answer to the nearest whole number.)
- A trader claims to sell vegetables at a profit of 52%, but also dishonestly uses a weight which is 8% less than what is mentioned on it. Find the total percentage of profit earned by the trader. (Round off the answer to the nearest whole number.)
A trader claims to sell fruits at a profit of 22%, but also dishonestly uses a weight which is 4% less than what is mentioned on it. Find the total percentage of profit earned by the trader. (Round off the answer to the nearest whole number.)
- A trader claims to sell pulses at a profit of 48%, but also dishonestly uses a weight which is 12% less than what is mentioned on it. Find the total percentage of profit earned by the trader. (Round off the answer to the nearest whole number.)
- A shopkeeper professes to sell his goods at a 20% loss but uses a false balance and gains 40%. The actual weight (rounded off to one decimal place) he uses for 1 kg is:
