A fan was sold for Rs. 3600 at a loss of 10%. What would be the gain or loss percent if it was sold for Rs. 4200?
Gain 5%
Understanding Profit and Loss Calculation
This problem involves calculating profit or loss percentage when the selling price of a fan changes, given an initial selling price and loss percentage.
First, we need to find the original cost price (CP) of the fan using the information from the first sale.
Calculating Cost Price from Selling Price and Loss
The fan was sold for Rs. 3600 at a loss of 10%. The formula relating Selling Price (SP), Cost Price (CP), and Loss Percentage is:
\(SP = CP \times (1 - \frac{\text{Loss \%}}{100})\)
We are given:
- Selling Price (SP\(_1\)) = Rs. 3600
- Loss % = 10%
Substitute these values into the formula:
\(3600 = CP \times (1 - \frac{10}{100})\)
\(3600 = CP \times (1 - 0.10)\)
\(3600 = CP \times 0.90\)
Now, we solve for CP:
\(CP = \frac{3600}{0.90}\)
\(CP = \frac{36000}{9}\)
\(CP = 4000\)
So, the cost price of the fan is Rs. 4000.
Determining Gain or Loss with New Selling Price
Now, consider the second scenario where the fan is sold for Rs. 4200.
- Cost Price (CP) = Rs. 4000
- New Selling Price (SP\(_2\)) = Rs. 4200
To determine if there is a gain or loss, we compare the new selling price with the cost price:
Since SP\(_2\) (Rs. 4200) is greater than CP (Rs. 4000), there is a gain.
The amount of gain is calculated as:
Gain Amount = New Selling Price - Cost Price
Gain Amount = \(4200 - 4000\)
Gain Amount = Rs. 200
Finally, we calculate the gain percentage using the formula:
\(\text{Gain \%} = \frac{\text{Gain Amount}}{CP} \times 100\)
Substitute the values:
\(\text{Gain \%} = \frac{200}{4000} \times 100\)
\(\text{Gain \%} = \frac{200}{40}\)
\(\text{Gain \%} = 5\)
The gain percentage is 5%.
Therefore, if the fan was sold for Rs. 4200, there would be a gain of 5%.
Revision Table: Profit and Loss Formulas
| Concept | Formula |
|---|---|
| Profit | SP > CP |
| Loss | SP < CP |
| Profit Amount | SP - CP |
| Loss Amount | CP - SP |
| Profit % | \(\frac{\text{Profit Amount}}{CP} \times 100\) |
| Loss % | \(\frac{\text{Loss Amount}}{CP} \times 100\) |
| Finding SP (Profit) | \(SP = CP \times (1 + \frac{\text{Profit \%}}{100})\) |
| Finding SP (Loss) | \(SP = CP \times (1 - \frac{\text{Loss \%}}{100})\) |
| Finding CP (Profit) | \(CP = \frac{SP}{1 + \frac{\text{Profit \%}}{100}}\) |
| Finding CP (Loss) | \(CP = \frac{SP}{1 - \frac{\text{Loss \%}}{100}}\) |
Additional Information on Profit and Loss Concepts
Understanding basic terms in profit and loss is crucial:
- Cost Price (CP): The price at which an article is purchased.
- Selling Price (SP): The price at which an article is sold.
- Profit: Occurs when Selling Price is greater than Cost Price. It is the gain made by the seller.
- Loss: Occurs when Selling Price is less than Cost Price. It is the amount lost by the seller.
- Profit Percentage: Profit expressed as a percentage of the Cost Price.
- Loss Percentage: Loss expressed as a percentage of the Cost Price.
All profit or loss percentages are typically calculated with respect to the Cost Price, unless otherwise specified.
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Important Questions from Successive Selling
By selling a watch at Rs. 840 a person loses 4%. Find the gain or loss if he sold it for Rs. 875?
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The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?
- The selling price of 24 articles is equal to the cost price of 26 articles. If, due to a change in market conditions, the selling price of each article decreases by $10\%$ and the cost price of each article increases by $5\%$, what will be the new gain or loss percentage (correct to two decimal places)?
Anil bought some articles at 6 for Rs. 8 and sold them at 10 for Rs. 12. His percentage loss or gain is:
