Question

A dishonest shopkeeper professes to sell his goods at cost price but uses a false weight of 920 grams for a 1 kg weight. What is his overall profit percentage?

• A. 8%
• B. 8.69%
• C. 7.41%
• D. 9.2%

Hint:

For dishonest dealing with false weights, remember the trick:
Profit % = $\frac{\text{Error}}{\text{Weight Used} - \text{Error}} \times 100$.
Error = $1000 - 920 = 80$ grams.
Weight Used = 920 grams.
Profit % = $\frac{80}{920} \times 100 = 8.69\%$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The problem describes a dishonest shopkeeper who claims to sell goods at the cost price (CP) but uses a false weight, effectively selling less quantity than he charges for. We need to calculate his actual profit percentage.

Step 2: Key Formula or Approach:
For such problems, it's easiest to assume a cost price per unit weight (e.g., per gram).
Let the cost price of 1 gram of goods be Re. 1.
1. Calculate the cost price of the quantity the shopkeeper actually sells.
2. Calculate the selling price for the quantity the shopkeeper claims to sell.
3. Calculate the profit.
4. Calculate the profit percentage based on the actual cost price.
Alternatively, a direct formula can be used:
\[ \text{Profit \%} = \left( \frac{\text{Error}}{\text{True Value} - \text{Error}} \right) \times 100 \]
Here, Error = (True Weight - False Weight) and True Value = True Weight (or 1000 grams).

Step 3: Detailed Explanation:
1. True Weight and False Weight:
True weight (what he should give) = 1 kg = 1000 grams.
False weight (what he actually gives) = 920 grams.
2. Assumed Cost Price:
Let the cost price (CP) of 1 gram of goods be Re. 1.
3. Shopkeeper's Actual Cost (for quantity sold):
The shopkeeper actually sells 920 grams of goods.
So, his actual cost price for this quantity is Rs. $920 \times 1 = \text{Rs. } 920$.
4. Shopkeeper's Selling Price (for quantity claimed):
He professes to sell at the cost price of 1 kg (1000 grams).
So, he charges the customer for 1000 grams at Re. 1/gram, which is Rs. $1000 \times 1 = \text{Rs. } 1000$.
5. Calculate Profit:
Profit = Selling Price - Actual Cost Price
Profit = Rs. $1000 - \text{Rs. } 920 = \text{Rs. } 80$.
6. Calculate Profit Percentage:
Profit % = $\left( \frac{\text{Profit}}{\text{Actual Cost Price}} \right) \times 100$
Profit % = $\left( \frac{80}{920} \right) \times 100$
Profit % = $\left( \frac{8}{92} \right) \times 100 = \left( \frac{2}{23} \right) \times 100$
Profit % = $\frac{200}{23} \approx 8.6956... \%$
Rounding to two decimal places, Profit % $\approx$ 8.69%.

Step 4: Final Answer:
His overall profit percentage is 8.69%.