A grocer claims that he is selling sugar at Rs. 48/kg, which costs him Rs. 50/kg, but he is giving 900 g instead of 1000 g. What will be the approximate percentage profit?
6.7%
Understanding the Dishonest Grocer Problem
This problem involves a grocer who uses deceptive practices to make a profit. He claims to sell sugar at a price lower than his cost price but compensates by giving a lower weight than what he charges for. To find the true profit percentage, we need to calculate the actual cost incurred by the grocer for the quantity of sugar he sells and the actual revenue he earns from that sale.
Calculating the Actual Cost Price
The grocer buys sugar at Rs. 50 per kg. A kilogram is 1000 grams. However, he only gives 900 grams to the customer while charging for 1 kg. So, we need to find out what was the grocer's cost for the 900 grams of sugar he actually sold.
- Cost of 1000 g = Rs. 50
- Cost of 1 g = $\frac{50}{1000}$ Rs.
- Cost of 900 g = $\frac{50}{1000} \times 900$ Rs.
Let's calculate the cost of 900 g:
Cost of 900 g = $\frac{50}{1000} \times 900 = \frac{50 \times 9}{10} = 5 \times 9 = 45$ Rs.
So, the actual cost price for the grocer for the amount of sugar he gives is Rs. 45.
Calculating the Actual Selling Price (Revenue)
The grocer claims to sell sugar at Rs. 48 per kg. He charges the customer based on the price for 1 kg, even though he only gives 900 g. Therefore, the actual revenue he collects for selling 900 g is the claimed price for 1 kg.
- Claimed Selling Price per kg (1000 g) = Rs. 48
- Actual Revenue for selling 900 g = Rs. 48
Determining the Profit Made
The profit is the difference between the actual revenue collected and the actual cost incurred for the quantity of sugar sold.
- Actual Revenue = Rs. 48
- Actual Cost = Rs. 45
- Profit = Actual Revenue - Actual Cost
- Profit = $48 - 45 = 3$ Rs.
The grocer makes a profit of Rs. 3 on every 900 g of sugar he sells using this method.
Calculating the Percentage Profit
The percentage profit is calculated based on the actual cost price.
Percentage Profit = $\frac{\text{Profit}}{\text{Actual Cost Price}} \times 100\%$
Percentage Profit = $\frac{3}{45} \times 100\%$
Percentage Profit = $\frac{1}{15} \times 100\%$
Percentage Profit = $\frac{100}{15}\%$
Percentage Profit = $\frac{20}{3}\%$
To find the approximate percentage profit, we convert the fraction to a decimal:
$\frac{20}{3} \approx 6.666...\%$
Rounding to one decimal place, the approximate percentage profit is 6.7%.
Summary of Calculation Steps
| Item | Value | Notes |
|---|---|---|
| Original Cost Price per kg | Rs. 50 | Cost for 1000 g |
| Actual Quantity Sold | 900 g | Weight given to customer |
| Actual Cost for 900 g | Rs. 45 | Calculated based on cost per 1000g |
| Claimed Selling Price per kg | Rs. 48 | Price charged for 900g |
| Actual Revenue for 900 g | Rs. 48 | This is the amount collected |
| Profit | Rs. 3 | Actual Revenue - Actual Cost |
| Percentage Profit | $\approx$ 6.7% | (Profit / Actual Cost) * 100% |
The calculated approximate percentage profit is 6.7%.
Revision Table: Profit and Loss Basics
| Term | Definition | Formula (if applicable) |
|---|---|---|
| Cost Price (CP) | The price at which an article is purchased. | - |
| Selling Price (SP) | The price at which an article is sold. | - |
| Profit | When SP > CP. | Profit = SP - CP |
| Loss | When CP > SP. | Loss = CP - SP |
| Profit Percentage | Profit expressed as a percentage of CP. | Profit % = ($\frac{\text{Profit}}{\text{CP}} \times 100$%) |
| Loss Percentage | Loss expressed as a percentage of CP. | Loss % = ($\frac{\text{Loss}}{\text{CP}} \times 100$%) |
Additional Information: Dishonest Shopkeepers
Problems involving dishonest shopkeepers often combine aspects of profit/loss with measurements (weights or volumes). The key is to always calculate the profit or loss based on the actual quantity sold or purchased and the actual money exchanged for that specific quantity.
- When a shopkeeper uses a false weight, the calculation of cost price and selling price needs to be adjusted for the actual weight used.
- If a shopkeeper claims to sell at cost price but uses false weights, they are still making a profit because the cost of the false weight quantity is less than the revenue received for the standard weight they charge for.
- Always find the cost and revenue for the same actual quantity of goods.
These types of problems test your ability to identify the true cost and revenue figures hidden behind the stated prices and weights.
Similar Questions
A shopkeeper sells an item at a profit of 15% and uses a weight which is 20% less. Find his actual profit percentage.
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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:
