A man sells his bike for Rs. 132000 earning a profit of 10%. If he had sold it for Rs, 126000, then what is his profit or loss percent?
5% profit
This problem involves calculating profit or loss percentage in two different scenarios for the same item, a bike. We are given the selling price and profit percentage for the first sale, which allows us to determine the original cost price of the bike. Once the cost price is known, we can analyze the second selling price to find the new profit or loss and express it as a percentage.
Calculating the Cost Price of the Bike
In the first scenario, the man sells his bike for Rs. 132000 and makes a profit of 10%. We can use the formula relating Selling Price (SP), Cost Price (CP), and Profit Percentage.
The formula for Selling Price when there is a profit is:
$$ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right) $$
We are given SP = Rs. 132000 and Profit % = 10%. Let's plug these values into the formula to find the Cost Price (CP).
$$ 132000 = \text{CP} \times \left(1 + \frac{10}{100}\right) $$
$$ 132000 = \text{CP} \times \left(1 + 0.10\right) $$
$$ 132000 = \text{CP} \times 1.10 $$
Now, we can solve for CP:
$$ \text{CP} = \frac{132000}{1.10} $$
$$ \text{CP} = 120000 $$
So, the cost price of the bike is Rs. 120000.
Analyzing the Second Sale Scenario
In the second scenario, the man considers selling the bike for Rs. 126000. We need to determine if this selling price (SP2) results in a profit or a loss compared to the calculated cost price (CP).
- Cost Price (CP) = Rs. 120000
- Selling Price (SP2) = Rs. 126000
Comparing SP2 and CP:
$$ \text{SP2} = 126000 $$
$$ \text{CP} = 120000 $$
Since SP2 > CP (126000 > 120000), the man would make a profit in this scenario.
The amount of profit is:
$$ \text{Profit} = \text{SP2} - \text{CP} $$
$$ \text{Profit} = 126000 - 120000 $$
$$ \text{Profit} = 6000 $$
The profit in the second scenario is Rs. 6000.
Calculating the Profit Percentage for the Second Sale
Now we calculate the profit percentage based on the profit amount and the cost price.
The formula for Profit Percentage is:
$$ \text{Profit \%} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 $$
We have Profit = Rs. 6000 and CP = Rs. 120000. Let's substitute these values:
$$ \text{Profit \%} = \left(\frac{6000}{120000}\right) \times 100 $$
Simplify the fraction:
$$ \text{Profit \%} = \left(\frac{6}{120}\right) \times 100 $$
$$ \text{Profit \%} = \left(\frac{1}{20}\right) \times 100 $$
$$ \text{Profit \%} = 0.05 \times 100 $$
$$ \text{Profit \%} = 5 $$
So, if the man had sold the bike for Rs. 126000, he would have made a 5% profit.
Summary of Calculations
| Scenario | Selling Price (SP) | Profit/Loss | Percentage |
|---|---|---|---|
| First Sale | Rs. 132000 | Profit | 10% |
| Second Sale (Hypothetical) | Rs. 126000 | Profit | 5% |
The cost price derived from the first sale is Rs. 120000. Selling the bike for Rs. 126000 results in a profit of Rs. 6000, which is a 5% profit when calculated on the cost price.
Revision Table: Profit and Loss Concepts
| Term | Definition | Formula (Profit) | Formula (Loss) |
|---|---|---|---|
| Cost Price (CP) | The price at which an article is purchased. | - | - |
| Selling Price (SP) | The price at which an article is sold. | SP = CP + Profit | SP = CP - Loss |
| Profit | When SP > CP (SP - CP) | Profit % = (Profit / CP) × 100 | - |
| Loss | When SP < CP (CP - SP) | - | Loss % = (Loss / CP) × 100 |
Additional Information: Importance of Cost Price
The cost price (CP) is a fundamental value in profit and loss calculations. Profit or loss percentage is always calculated with respect to the cost price unless stated otherwise. Understanding how to find the cost price from given information (like SP and profit/loss percentage) is crucial for solving problems involving changes in selling price or multiple transactions. In this problem, finding the initial cost price of Rs. 120000 was the key step to determine the outcome of the second hypothetical sale at Rs. 126000 and calculate the profit percentage.
Important Questions from Profit and Loss
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
