A dishonest dealer professes to sell goods at the cost price, but uses a false weight of 900 grams instead of a kilogram. His gain percentage is:
\(11\frac{1}{9}\)%
Understanding the Dishonest Dealer's Trick
This question describes a common scenario where a seller aims to profit by deceiving customers about the quantity of goods. The dealer claims to sell items at the original cost price but uses a false weight. In this case, the dealer uses a 900-gram weight instead of the standard 1000-gram kilogram weight.
Calculating the Gain Percentage
To determine the dealer's actual gain percentage, we need to compare what the dealer pays for the goods (Cost Price, CP) versus what the customer pays (Selling Price, SP). The key is that the dealer charges based on 1000 grams but only provides 900 grams.
Step 1: Determine the Actual Cost Price (CP)
Let's assume the cost price for 1 gram of the item is Re 1. Since the dealer delivers only 900 grams, the actual cost incurred by the dealer for the goods sold is the cost of 900 grams.
Actual CP = Cost of 900 grams = 900 grams \( \times \) Re 1/gram = Rs 900.
Step 2: Determine the Selling Price (SP)
The dealer claims to sell at the cost price. This implies he charges the price equivalent to 1000 grams, even though he only hands over 900 grams. The price charged is thus the price for 1000 grams.
SP = Price charged for 1000 grams = 1000 grams \( \times \) Re 1/gram = Rs 1000.
Step 3: Calculate the Gain
The gain is the difference between the Selling Price (what the customer pays) and the Cost Price (what the dealer actually spent on the goods provided).
Gain = SP - CP
Gain = Rs 1000 - Rs 900 = Rs 100.
Step 4: Calculate the Gain Percentage
The gain percentage is always calculated on the Cost Price (CP).
Gain Percentage = \( \frac{\text{Gain}}{\text{CP}} \times 100 \) %
Substitute the values we found:
Gain Percentage = \( \frac{100}{900} \times 100 \) %
Simplify the fraction:
Gain Percentage = \( \frac{1}{9} \times 100 \) %
Gain Percentage = \( \frac{100}{9} \) %
Step 5: Express the Gain Percentage as a Mixed Fraction
To convert the improper fraction \( \frac{100}{9} \) % into a mixed fraction, divide 100 by 9:
\( 100 \div 9 = 11 \) with a remainder of 1.
Therefore, \( \frac{100}{9} \) % is equal to \( 11\frac{1}{9} \) %.
Summary of Calculation
| Component | Value (in Rs) |
| Actual Cost Price (CP) for 900g goods | 900 |
| Selling Price (SP) charged (price for 1000g) | 1000 |
| Gain (SP - CP) | 100 |
| Gain Percentage (on CP) | \(11\frac{1}{9}\)% |
The dishonest dealer makes a gain of \(11\frac{1}{9}\)% by using a false weight.
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