Ramesh claims that he is selling onions at Rs. 36 per kg, which costs him Rs. 40 per kg, but he gives 800 grams instead of 1 kg. Find Ramesh's percentage gain or loss.
Understanding the Problem: Dishonest Selling with False Weight
This problem involves a scenario where a seller, Ramesh, is using a dishonest practice. He claims to sell onions at a price lower than his cost price, which would normally result in a loss. However, he compensates for this claimed loss by giving a lesser quantity (800 grams) than what the customer pays for (1 kg).
To find his actual gain or loss, we need to compare the actual cost of the quantity of onions he sells (800 grams) with the actual amount of money he receives for selling that quantity.
Calculating the Actual Cost Price
Ramesh buys onions at Rs. 40 per kg. He sells 800 grams to the customer. We need to find the cost price of these 800 grams.
- Cost of 1 kg (1000 grams) = Rs. 40
- Cost of 1 gram = \( \frac{40}{1000} \) Rupees
- Cost of 800 grams = \( \frac{40}{1000} \times 800 \) Rupees
- Actual Cost Price (CP) for 800 grams = \( \frac{40 \times 800}{1000} = \frac{32000}{1000} = 32 \) Rupees
So, the actual cost of the onions Ramesh sold is Rs. 32.
Calculating the Actual Selling Price
Ramesh tells the customer he is selling at Rs. 36 per kg. The customer pays for 1 kg, assuming they are getting 1 kg at this price. Even though the customer receives only 800 grams, Ramesh collects money as if he sold 1 kg at the claimed price.
- Claimed Selling Price (SP) per kg = Rs. 36
- Amount collected from the customer (for what is charged as 1 kg) = Rs. 36
This Rs. 36 is the actual selling price received for the 800 grams of onions.
Finding the Gain or Loss Amount
Now we compare the actual selling price (SP) with the actual cost price (CP) for the 800 grams sold.
- Actual Selling Price (SP) = Rs. 36
- Actual Cost Price (CP) = Rs. 32
Since the Actual SP (Rs. 36) is greater than the Actual CP (Rs. 32), Ramesh makes a gain.
- Gain = Actual SP - Actual CP
- Gain = Rs. 36 - Rs. 32 = Rs. 4
Ramesh makes a gain of Rs. 4 on the transaction of selling 800 grams.
Calculating the Percentage Gain
The percentage gain is calculated on the actual cost price of the quantity sold.
- Percentage Gain = \( \left( \frac{\text{Gain}}{\text{Actual CP}} \right) \times 100\% \)
- Percentage Gain = \( \left( \frac{4}{32} \right) \times 100\% \)
- Percentage Gain = \( \left( \frac{1}{8} \right) \times 100\% \)
- Percentage Gain = \( 0.125 \times 100\% = 12.5\% \)
Ramesh's percentage gain is 12.5%.
Summary of Calculation Steps
| Step | Description | Calculation | Result |
|---|---|---|---|
| 1 | Actual Cost of 800g | \( \frac{40}{1000} \times 800 \) | Rs. 32 |
| 2 | Actual Selling Price received | Rs. 36 (Charged for 1kg at Rs. 36/kg) | Rs. 36 |
| 3 | Gain Amount | Actual SP - Actual CP = \( 36 - 32 \) | Rs. 4 |
| 4 | Percentage Gain | \( \left( \frac{\text{Gain}}{\text{Actual CP}} \right) \times 100 \) = \( \left( \frac{4}{32} \right) \times 100 \) | 12.5% |
The final result shows a percentage gain of 12.5%.
Revision Table: Key Concepts in Profit and Loss
| Term | Definition | Formula/Relation |
|---|---|---|
| Cost Price (CP) | The price at which an article is purchased. | - |
| Selling Price (SP) | The price at which an article is sold. | - |
| Gain (Profit) | When Selling Price > Cost Price. | Gain = SP - CP |
| Loss | When Cost Price > Selling Price. | Loss = CP - SP |
| Percentage Gain | Gain calculated as a percentage of the Cost Price. | \( \% \text{Gain} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \) |
| Percentage Loss | Loss calculated as a percentage of the Cost Price. | \( \% \text{Loss} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \) |
Additional Information: Dealing with False Weights
Problems involving false weights are common variations of profit and loss questions. The key is always to compare the actual cost of the quantity delivered with the amount received from the customer.
- Assume a base quantity (like 1 kg or 1000 grams).
- Calculate the cost price of the quantity actually sold (e.g., 800 grams).
- Calculate the selling price received for the quantity charged for (e.g., charging for 1 kg, even if less is given).
- Compare the actual cost and actual selling price to find the gain or loss.
- Calculate the percentage gain or loss based on the actual cost price.
In this specific case, Ramesh gives 800g but charges for 1000g. His cost is for 800g, but his revenue is based on charging for 1000g (at a discounted rate). The calculation reflects this difference.
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:
