Understanding the Vendor's Claim and Cheating
The problem involves a vendor who claims to sell wheat at a specific loss percentage but uses incorrect weights to increase their actual profit.
Calculating Actual Profit Percentage
We need to find the vendor's real profit percentage considering both the claimed loss and the weight discrepancy.
Step 1: Define Variables and Base Cost
Let the cost price (CP) of 1 unit of weight be $1$. Assume the vendor claims to sell $W$ units of weight.
- The cost price for $W$ units is assumed to be $W \times 1 = W$.
- The vendor claims a 50% loss. This means the Selling Price (SP) is 50% of the cost price.
- Claimed SP for $W$ units = $W \times (1 - 0.50) = 0.5W$.
Step 2: Account for Cheating in Weights
The vendor uses weights that are 65% less than the stated weight ($W$).
- Actual weight used by the vendor = $W \times (1 - 0.65) = W \times 0.35 = 0.35W$.
- The actual cost incurred by the vendor is for this reduced weight: Actual CP = $0.35W \times 1 = 0.35W$.
Step 3: Determine Actual Revenue and Profit
The vendor receives the selling price based on the *claimed* weight ($W$), not the actual weight supplied.
- Actual Revenue = Claimed SP = $0.5W$.
- Actual Profit = Actual Revenue - Actual CP
- Actual Profit = $0.5W - 0.35W = 0.15W$.
Step 4: Calculate the Actual Profit Percentage
The profit percentage is calculated based on the *actual cost* incurred by the vendor.
- Actual Profit Percentage = $\frac{\text{Actual Profit}}{\text{Actual CP}} \times 100$
- Actual Profit Percentage = $\frac{0.15W}{0.35W} \times 100$
- Actual Profit Percentage = $\frac{0.15}{0.35} \times 100 = \frac{15}{35} \times 100 = \frac{3}{7} \times 100$
- Actual Profit Percentage $\approx 0.42857 \times 100 = 42.857\%$
Step 5: Round the Result
Rounding the calculated profit percentage to two decimal places:
- Actual Profit Percentage $\approx 42.86\%$
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:
