A shopkeeper sells an item at a profit of 15% and uses a weight which is 20% less. Find his actual profit percentage.
43.75%
Calculating Actual Profit with False Weight
This problem involves calculating the actual profit percentage a shopkeeper makes when they both mark up the price and use a false weight. We need to consider the cost price of the quantity actually sold versus the selling price received for that quantity.
Let's break down the problem step-by-step:
- Assume a base value for the quantity the customer is supposed to receive and its cost.
- Calculate the selling price based on the announced profit percentage.
- Calculate the actual quantity the shopkeeper sells using the false weight.
- Calculate the actual cost price of the quantity actually sold.
- Determine the actual profit.
- Calculate the actual profit percentage based on the actual cost price.
Step 1: Assume Base Values
Let's assume the shopkeeper buys the item at a cost of ₹1 per gram.
Let's assume the customer intends to buy 1000 grams (or 1 kg).
The Cost Price (CP) of 1000 grams for the shopkeeper is \(₹1 \times 1000 = ₹1000\).
Step 2: Calculate Selling Price with Announced Profit
The shopkeeper announces a profit of 15%. This profit is calculated on the price the customer pays for the quantity they believe they are getting (1000 grams).
Selling Price (SP) = CP + Profit
SP = \(₹1000 + 15\%\) of \(₹1000\)
SP = \(₹1000 + \frac{15}{100} \times ₹1000\)
SP = \(₹1000 + ₹150\)
SP = \(₹1150\)
So, the customer pays ₹1150 for the quantity they think is 1000 grams.
Step 3: Calculate Actual Quantity Sold with False Weight
The shopkeeper uses a weight that is 20% less than the intended weight (1000 grams).
Reduced weight = 20% of 1000 grams
Reduced weight = \(\frac{20}{100} \times 1000 = 200\) grams
Actual weight used = Intended weight - Reduced weight
Actual weight used = \(1000 \text{ grams} - 200 \text{ grams} = 800 \text{ grams}\)
The shopkeeper actually sells only 800 grams to the customer.
Step 4: Calculate Actual Cost Price of Quantity Sold
The shopkeeper's cost price is ₹1 per gram.
The actual quantity sold is 800 grams.
Actual Cost Price (Actual CP) = Cost per gram \(\times\) Actual weight sold
Actual CP = \(₹1 \times 800 \text{ grams} = ₹800\)
Step 5: Determine Actual Profit
The shopkeeper receives ₹1150 (the Selling Price calculated in Step 2) for the 800 grams actually sold (costing ₹800).
Actual Profit = Selling Price - Actual Cost Price
Actual Profit = \(₹1150 - ₹800 = ₹350\)
Step 6: Calculate Actual Profit Percentage
The actual profit percentage is calculated based on the Actual Cost Price.
Actual Profit Percentage = \(\frac{\text{Actual Profit}}{\text{Actual CP}} \times 100\%\)
Actual Profit Percentage = \(\frac{₹350}{₹800} \times 100\%\)
Actual Profit Percentage = \(\frac{350}{800} \times 100\%\)
Actual Profit Percentage = \(\frac{35}{80} \times 100\%\)
Actual Profit Percentage = \(\frac{35}{8} \times 10\%\)
Actual Profit Percentage = \(\frac{350}{8}\%\)
Actual Profit Percentage = \(\frac{175}{4}\%\)
Actual Profit Percentage = \(43.75\%\)
The shopkeeper's actual profit percentage is 43.75%.
| Parameter | Value |
|---|---|
| Assumed Cost Price per gram | ₹1 |
| Intended Weight (Customer Perception) | 1000 grams |
| CP of Intended Weight | ₹1000 |
| Announced Profit Percentage | 15% |
| Selling Price for Intended Weight | ₹1150 |
| Weight Reduction Percentage | 20% |
| Actual Weight Used | 800 grams |
| Actual CP of Actual Weight Used | ₹800 |
| Actual Profit | ₹350 |
| Actual Profit Percentage | 43.75% |
Revision Table: Key Concepts in Profit and Loss
| Term | Definition | Formula (Basic) |
|---|---|---|
| Cost Price (CP) | The price at which an item is bought. | - |
| Selling Price (SP) | The price at which an item is sold. | - |
| Profit | When SP > CP. | Profit = SP - CP |
| Loss | When SP < CP. | Loss = CP - SP |
| Profit Percentage | Profit expressed as a percentage of CP. | \(\frac{\text{Profit}}{\text{CP}} \times 100\%\) |
| Loss Percentage | Loss expressed as a percentage of CP. | \(\frac{\text{Loss}}{\text{CP}} \times 100\%\) |
| False Weight / Dishonest Dealer | Selling less quantity than promised, while charging for the promised quantity. | Actual CP is based on weight sold, SP is based on weight promised. |
Additional Information on Dishonest Dealing Problems
Problems involving dishonest shopkeepers using false weights are common variations of profit and loss questions. The key is to understand that the profit comes from two sources:
- The markup on the price.
- Selling less quantity for the price of a larger quantity.
The actual profit percentage is always calculated on the actual cost incurred by the shopkeeper, which is the cost of the quantity they actually sell.
A general formula can sometimes be derived for specific cases, but understanding the basic principle (comparing Actual CP of quantity sold with SP received) is usually more flexible for different problem variations.
In this case, the shopkeeper gains by selling at a 15% markup (charging ₹1150 instead of ₹1000 if they sold the full weight) and also gains by selling only 800g while charging for 1000g. The total gain of ₹350 is on an actual investment (cost) of ₹800.
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:
