Understanding Dishonest Dealer Calculations

This question involves a classic scenario of a dishonest dealer who uses a false weight while also claiming to sell at a loss. To determine the actual profit or loss percentage, we need to consider both the claimed loss on the cost price and the gain made by using a lesser weight.

Analyzing the Question: False Weight and Claimed Loss

The dealer makes two statements/actions:

• Claims to sell at a 15% loss on the cost price.
• Uses a weight of 20 g instead of the promised 25 g.

This means the customer pays for 25 g, based on a price calculation that includes a 15% loss on the cost of 25 g. However, the dealer only provides 20 g of goods. The dealer's actual cost is only for the 20 g supplied, not the 25 g the customer is charged for.

Step-by-Step Calculation of Profit/Loss Percentage

Let's assume a convenient cost price per gram to make the calculation easy. Suppose the cost price of 1 gram is & रुपया;1.

1. Calculate the Cost Price of the Claimed Weight:
   The dealer claims to sell 25 g. The cost price of 25 g would be \(25 \times \text{& रुपया;1} = \text{& रुपया;25}\).
2. Calculate the Selling Price based on Claimed Loss:
   The dealer claims a 15% loss on the cost price of 25 g.
   Selling Price = Cost Price of 25 g - 15% of Cost Price of 25 g
   Selling Price = \(\text{& रुपया;25} - 0.15 \times \text{& रुपया;25}\)
   Selling Price = \(\text{& रुपया;25} (1 - 0.15)\)
   Selling Price = \(\text{& रुपया;25} \times 0.85\)
   Selling Price = \(\text{& रुपया;}21.25\)
   So, the customer pays & रुपया;21.25 for what they believe is 25 g.
3. Calculate the Actual Cost Price of the Goods Sold:
   The dealer actually provides only 20 g of goods.
   Actual Cost Price = Cost price of 20 g
   Actual Cost Price = \(20 \times \text{& रुपया;1} = \text{& रुपया;20}\).
4. Determine the Profit or Loss:
   The dealer sells goods that cost & रुपया;20 for & रुपया;21.25.
   Since the Selling Price (& रुपया;21.25) is greater than the Actual Cost Price (& रुपया;20), the dealer makes a profit.
   Profit = Selling Price - Actual Cost Price
   Profit = \(\text{& रुपया;}21.25 - \text{& रुपया;}20\)
   Profit = \(\text{& रुपया;}1.25\)
5. Calculate the Profit Percentage:
   The profit percentage is calculated on the actual cost price.
   Profit Percentage = \(\left( \frac{\text{Profit}}{\text{Actual Cost Price}} \right) \times 100 \%\)
   Profit Percentage = \(\left( \frac{\text{& रुपया;}1.25}{\text{& रुपया;}20} \right) \times 100 \%\)
   Profit Percentage = \(\left( \frac{1.25}{20} \right) \times 100 \%\)
   Profit Percentage = \(\left( \frac{5/4}{20} \right) \times 100 \%\)
   Profit Percentage = \(\left( \frac{5}{4 \times 20} \right) \times 100 \%\)
   Profit Percentage = \(\left( \frac{5}{80} \right) \times 100 \%\)
   Profit Percentage = \(\left( \frac{1}{16} \right) \times 100 \%\)
   Profit Percentage = \(\frac{100}{16} \%\)
   Profit Percentage = \(\frac{25}{4} \%\)
   Profit Percentage = \(6.25 \%\)

Conclusion on Profit or Loss

Based on the calculations, the dishonest dealer makes a profit of 6.25%. The gain from using a false weight outweighs the claimed loss on the cost price.

Revision Table: Dishonest Dealer Problems & Concepts

Additional Information: Solving False Weight Questions

Problems involving dishonest dealers and false weights are common in competitive exams. The key is to always differentiate between what the dealer claims and what they actually do.

• Assume a base value (like cost per gram) or use variables to represent costs. This simplifies the calculation.
• Clearly identify the actual quantity of goods sold versus the quantity claimed.
• Calculate the selling price based on the *claimed* quantity and *claimed* profit/loss.
• Calculate the *actual* cost price based on the *actual* quantity delivered.
• Compare the selling price and actual cost price to find the true profit or loss.
• Always calculate the profit or loss percentage on the actual cost price.

These steps help in systematically approaching such problems and avoiding confusion between claimed and actual values.