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.)
Solving the Trader's Profit Problem
This question requires us to calculate the overall profit percentage a trader makes when they claim a certain profit margin (22%) but also use a scale that shows a weight less than the actual amount sold (4% less). We need to combine these two factors to find the real profit.
Understanding the Core Concepts
To solve this, we need to understand two main ideas:
- Claimed Profit: The trader states they are making a 22% profit. This usually means they are setting their selling price 22% higher than the cost price for the quantity they *claim* to sell.
- Dishonest Weight: The trader uses a faulty scale. They mention a weight (e.g., 1 kg), but the actual weight they provide is less (4% less in this case). This means they incur a lower cost price for the goods they actually hand over.
- Combined Profit: The final profit percentage depends on both the markup on the price and the reduction in the quantity given.
Step-by-Step Calculation for Profit Percentage
Let's break down the calculation step-by-step. We can assume a convenient cost price and quantity to make calculations easier.
1. Assume a Base Cost and Quantity:
Assume the cost price (CP) of the fruits is $1 per gram. Let's also assume the trader *claims* to sell 1000 grams.
2. Calculate the Selling Price (SP) Based on the Claimed Profit:
The cost price for the 1000 grams the trader claims to sell is: $ \text{CP}_{\text{claimed}} = 1000 \text{ grams} \times \$1/\text{gram} = \$1000 $ The trader claims a 22% profit on this. So, the selling price they set for 1000 grams is: $ \text{SP}_{\text{marked}} = \text{CP}_{\text{claimed}} \times (1 + \frac{22}{100}) $ $ \text{SP}_{\text{marked}} = \$1000 \times (1 + 0.22) = \$1000 \times 1.22 = \$1220 $ This means the trader wants to receive $1220 for what they present as 1000 grams.
3. Determine the Actual Quantity Sold:
The trader uses a weight that is 4% less than mentioned. So, for the 1000 grams mentioned on the scale, the actual weight provided is: $ \text{Actual Weight} = 1000 \text{ grams} \times (1 - \frac{4}{100}) $ $ \text{Actual Weight} = 1000 \times (1 - 0.04) = 1000 \times 0.96 = 960 \text{ grams} $ The customer only receives 960 grams.
4. Calculate the Actual Cost Price (CP) for the Goods Actually Sold:
The cost for the 960 grams that the trader actually gives to the customer is: $ \text{Actual CP} = 960 \text{ grams} \times \$1/\text{gram} = \$960 $
5. Identify the Actual Selling Price (SP) Received:
The trader sells the 960 grams but charges the price they intended for 1000 grams ($1220). $ \text{Actual SP} = \$1220 $
6. Calculate the Actual Profit:
The profit is the difference between the actual selling price and the actual cost price for the goods sold: $ \text{Actual Profit} = \text{Actual SP} - \text{Actual CP} $ $ \text{Actual Profit} = \$1220 - \$960 = \$260 $
7. Calculate the Total Percentage Profit:
The total percentage profit is calculated based on the *actual cost price* incurred by the trader:
$ \text{Total Profit Percentage} = (\frac{\text{Actual Profit}}{\text{Actual CP}}) \times 100 $ $ \text{Total Profit Percentage} = (\frac{\$260}{\$960}) \times 100 $ To simplify the fraction $ \frac{260}{960} $, we can divide both numerator and denominator by 10: $ \frac{26}{96} $. Further simplifying by dividing by 2: $ \frac{13}{48} $. $ \text{Total Profit Percentage} = \frac{13}{48} \times 100 $ $ \text{Total Profit Percentage} \approx 27.0833\% $8. Round the Result:
The question asks to round the answer to the nearest whole number. Rounding $27.0833\%$ gives 27%.
| Step | Description | Calculation/Value |
|---|---|---|
| 1 | Assumed Base CP per gram | $1 |
| 2 | Assumed Quantity Mentioned | 1000g |
| 3 | CP for Mentioned Quantity (1000g) | $1000 |
| 4 | Selling Price for Mentioned Quantity (1000g) | $1000 \times 1.22 = \$1220$ |
| 5 | Actual Quantity Sold (4% less) | $1000 \times 0.96 = 960$g |
| 6 | Actual CP for Goods Sold (960g) | $960 \times \$1 = \$960$ |
| 7 | Actual SP Received (Price for 1000g) | $1220 |
| 8 | Actual Profit | $1220 - \$960 = \$260$ |
| 9 | Total Profit Percentage | $(\$260 / \$960) \times 100 \approx 27.08\%$ |
| 10 | Rounded Profit Percentage | 27% |
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 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:
- A shopkeeper professes to sell his goods at a 60% loss but uses a false balance and gains 70%. The actual weight (rounded off to one decimal place) that he uses instead of 1 kg is:
