Question

A vendor claims to sell wheat at a loss of 25%. But he cheats by using weights that weigh 55% less than what is mentioned on them. What is his profit percentage (rounded off to 2 decimal places)?

• A. 66.89
• B. 66.78
• C. 66.66
• D. 66.79

Answer 1

Answer:

C. 66.66

1. Understand the Cheating:

• The vendor uses weights that are 55% less than what they claim. This means if the weight says "1 kg," it actually weighs only 45% of 1 kg (100% - 55% = 45%).

2. Set Up a Scenario:

• To make the calculations easier, let's assume the vendor intends to sell 100 kg of wheat.

• However, due to the faulty weights, he's actually selling only 45 kg of wheat.

3. Account for the Claimed Loss:

• The vendor claims a 25% loss. This means if the cost price of 100 kg of wheat is "X," he's selling it for 75% of "X" (100% - 25% = 75%). So the selling price is 0.75X.

4. Calculate the Actual Cost:

• The vendor is only providing 45 kg of wheat, not 100 kg. Therefore, the actual cost to him is only the cost of 45 kg.

• We can say that the cost of 1kg of wheat is X/100, therefore the cost of 45kg of wheat is 45×(X/100) = 0.45X

5. Calculate the Actual Profit:

• The selling price is 0.75X.

• The actual cost is 0.45X.

• The profit is 0.75X - 0.45X = 0.30X.

6. Calculate the Profit Percentage:

• Profit Percentage = (Profit / Actual Cost) × 100

• Profit Percentage = (0.30X / 0.45X) × 100

• Profit Percentage = (30/45) × 100

• Profit Percentage = (2/3) × 100

• Profit Percentage = 66.666...%

7. Round to Two Decimal Places:

• The profit percentage is approximately 66.66%.

Therefore, the vendor's actual profit percentage is approximately 66.66%.