A Shopkeeper loses 10% on selling an article for Rs. 360. To gain 30%, what should have been selling price of the article?
Rs. 520
Calculating Selling Price for Profit Gain
This problem involves calculating the cost price of an article when there is a loss and then determining the new selling price required to achieve a desired profit percentage. We will use the concepts of Cost Price (CP), Selling Price (SP), Loss Percentage, and Profit Percentage.
Understanding Key Terms in Profit and Loss
- Cost Price (CP): The price at which an article is purchased.
- Selling Price (SP): The price at which an article is sold.
- Loss: Occurs when SP < CP. Loss % = \(\frac{\text{Loss}}{\text{CP}} \times 100\)
- Profit (Gain): Occurs when SP > CP. Profit % = \(\frac{\text{Profit}}{\text{CP}} \times 100\)
Step-by-Step Solution to Find the New Selling Price
Step 1: Calculate the Cost Price (CP)
We are given that the shopkeeper sells the article for Rs. 360 and incurs a 10% loss. The formula relating SP, CP, and Loss % is:
\(\text{SP} = \text{CP} \times \left(\frac{100 - \text{Loss \%}}{100}\right)\)
Substituting the given values:
\(360 = \text{CP} \times \left(\frac{100 - 10}{100}\right)\)
\(360 = \text{CP} \times \left(\frac{90}{100}\right)\)
To find CP, we rearrange the formula:
\(\text{CP} = \frac{360 \times 100}{90}\)
\(\text{CP} = \frac{36000}{90}\)
\(\text{CP} = 400\)
So, the Cost Price of the article is Rs. 400.
Step 2: Calculate the New Selling Price for a 30% Gain
Now, the shopkeeper wants to gain 30% on the article. We know the CP is Rs. 400. The formula relating New SP, CP, and Gain % is:
\(\text{New SP} = \text{CP} \times \left(\frac{100 + \text{Gain \%}}{100}\right)\)
Substituting the values (CP = Rs. 400, Gain % = 30):
\(\text{New SP} = 400 \times \left(\frac{100 + 30}{100}\right)\)
\(\text{New SP} = 400 \times \left(\frac{130}{100}\right)\)
\(\text{New SP} = \frac{400 \times 130}{100}\)
\(\text{New SP} = 4 \times 130\)
\(\text{New SP} = 520\)
Therefore, to gain 30%, the selling price of the article should be Rs. 520.
Summary of Calculations
| Description | Value |
|---|---|
| Initial Selling Price (SP) | Rs. 360 |
| Initial Loss Percentage | 10% |
| Calculated Cost Price (CP) | Rs. 400 |
| Desired Gain Percentage | 30% |
| New Selling Price (New SP) | Rs. 520 |
Based on the calculations, the selling price should be Rs. 520 to achieve a 30% gain.
Revision Table: Profit and Loss Formulas
| Concept | Formula |
|---|---|
| Profit | SP - CP (if SP > CP) |
| Loss | CP - SP (if CP > SP) |
| Profit % | \(\frac{\text{Profit}}{\text{CP}} \times 100\) |
| Loss % | \(\frac{\text{Loss}}{\text{CP}} \times 100\) |
| SP when Profit % is known | \(\text{CP} \times \left(\frac{100 + \text{Profit \%}}{100}\right)\) |
| SP when Loss % is known | \(\text{CP} \times \left(\frac{100 - \text{Loss \%}}{100}\right)\) |
| CP when SP and Profit % are known | \(\text{SP} \times \left(\frac{100}{100 + \text{Profit \%}}\right)\) |
| CP when SP and Loss % are known | \(\text{SP} \times \left(\frac{100}{100 - \text{Loss \%}}\right)\) |
Additional Information: Calculating Percentage Changes
Percentage change is a way to express how much a quantity changes relative to its original value. In profit and loss, the base for calculating profit or loss percentage is always the Cost Price (CP).
If a value increases by P%, the new value is Original Value \(\times (1 + \frac{P}{100})\).
If a value decreases by L%, the new value is Original Value \(\times (1 - \frac{L}{100})\).
In our problem:
- When the shopkeeper lost 10%, the Selling Price (Rs. 360) was the Cost Price decreased by 10%: \(360 = \text{CP} \times (1 - \frac{10}{100}) = \text{CP} \times 0.90\).
- When the shopkeeper wants to gain 30%, the New Selling Price will be the Cost Price increased by 30%: \(\text{New SP} = \text{CP} \times (1 + \frac{30}{100}) = \text{CP} \times 1.30\).
Using these factors:
From \(360 = \text{CP} \times 0.90\), we get \(\text{CP} = \frac{360}{0.90} = 400\).
Then, \(\text{New SP} = 400 \times 1.30 = 520\).
This method gives the same result and is a quick way to handle percentage increases and decreases in profit and loss calculations.
Important Questions from Successive Selling
A dealer sold an article at a loss of 2%. Had he sold it for Rs. 44 more, he would have gained 20%. Find the cost price of the article
Radha purchased a Computer table for Rs. 10000 and a Centre table for Rs. 5000. She sold Computer table with 8% profit. With what profit percent should she sell the Centre table so as to gain 10% on the whole transaction.
If selling price of 75 articles is equal to cost price of 60 articles, then the approximate loss or gain percent is :
A.T.V. is sold at 8% gain. Had it been sold for Rs.2553 less; there would have been loss of 15%. To gain 18%, the selling price (in Rs.) of T.V. would be:
Some fruits are bought at 15 for Rs. 140 and an equal number of fruits at 10 for Rs. 120. If all the fruits are sold at Rs. 132 per dozen, then what is the profit percent in the entire transaction?
