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 merchant claims that he sells his goods at CP. But uses a weight of 900 g for the 1 kg weight. find his gain %
A shopkeeper cheats to the extent of 9% while buying and selling fruits, by using tampered weights. His total gain in percentage is:
A. 18.25
B. 18.81
C. 19.78
D. 18.5
What is the faulty weight used by a dishonest shopkeeper instead of the original weight of 1 kg to get a profit of 25%?
A dishonest financier claims to be lending money at simple interest, but he includes the interest every four months for calculating the principal. If he is charging an interest of 3%, the effective rate of interest becomes:
A dishonest shopkeeper claims to sell rice at the cost price of ₹95 per kg, but the weight he uses has 1 kg written on it, while it actually weighs 950 g. The profit he thus earns on selling rice having an actual weight of 95 kg rice is:
