Junko sold an item for Rs. 220 at a loss of 12%. By how much should she have raised the selling price above the cost price to make a profit of 10%?
Rs. 25
Understanding the Problem: Profit and Loss Calculation
The question asks us to determine how much higher the selling price should have been compared to the cost price to achieve a 10% profit, given that the item was initially sold at a 12% loss for Rs. 220.
To solve this, we first need to find the original cost price (CP) of the item. Then, we calculate the desired selling price (SP) for a 10% profit. Finally, we find the difference between this desired SP and the CP.
Step 1: Calculate the Cost Price (CP)
We are given the selling price (SP) and the loss percentage. The formula relating SP, CP, and loss percentage is:
\(\text{SP} = \text{CP} \times (1 - \text{Loss \% / 100})\)
We are given:
- Selling Price (SP) = Rs. 220
- Loss Percentage = 12%
Substituting the values into the formula:
\(220 = \text{CP} \times (1 - 12 / 100)\)
\(220 = \text{CP} \times (1 - 0.12)\)
\(220 = \text{CP} \times 0.88\)
Now, we solve for CP:
\(\text{CP} = \frac{220}{0.88}\)
\(\text{CP} = \frac{22000}{88}\)
\(\text{CP} = \text{Rs. } 250\)
So, the cost price of the item was Rs. 250.
Step 2: Calculate the Selling Price for 10% Profit
Now that we have the cost price, we need to find the selling price (let's call it SP') required to make a 10% profit. The formula relating SP', CP, and profit percentage is:
\(\text{SP'} = \text{CP} \times (1 + \text{Profit \% / 100})\)
We know:
- Cost Price (CP) = Rs. 250
- Desired Profit Percentage = 10%
Substituting the values:
\(\text{SP'} = 250 \times (1 + 10 / 100)\)
\(\text{SP'} = 250 \times (1 + 0.10)\)
\(\text{SP'} = 250 \times 1.10\)
\(\text{SP'} = \text{Rs. } 275\)
To make a profit of 10%, Junko should have sold the item for Rs. 275.
Step 3: Find the Difference Above Cost Price
The question asks by how much the selling price (for 10% profit) should have been raised above the cost price. This is the difference between the desired selling price (SP') and the cost price (CP).
Difference = SP' - CP
Difference = Rs. 275 - Rs. 250
Difference = Rs. 25
Therefore, Junko should have raised the selling price by Rs. 25 above the cost price to make a profit of 10%.
Summary of Calculations
| Description | Value |
|---|---|
| Initial Selling Price (with 12% loss) | Rs. 220 |
| Calculated Cost Price (CP) | Rs. 250 |
| Desired Selling Price (for 10% profit) | Rs. 275 |
| Amount SP' is above CP | Rs. 275 - Rs. 250 = Rs. 25 |
The selling price should have been Rs. 25 above the cost price to achieve a 10% profit.
Revision Table: Key Concepts
| Concept | Formula | Explanation |
|---|---|---|
| Loss | CP - SP | When Selling Price is less than Cost Price. |
| Loss Percentage | \(\frac{\text{Loss}}{\text{CP}} \times 100\) | Loss calculated as a percentage of Cost Price. |
| Profit | SP - CP | When Selling Price is greater than Cost Price. |
| Profit Percentage | \(\frac{\text{Profit}}{\text{CP}} \times 100\) | Profit calculated as a percentage of Cost Price. |
| SP with Loss | \(\text{CP} \times (1 - \text{Loss \% / 100})\) | Selling Price when there is a percentage loss. |
| SP with Profit | \(\text{CP} \times (1 + \text{Profit \% / 100})\) | Selling Price when there is a percentage profit. |
Additional Information: Profit and Loss Fundamentals
Profit and loss calculations are fundamental concepts in business and mathematics. They help in understanding the financial outcome of selling an item.
- Cost Price (CP): This is the original price at which an item is bought or manufactured.
- Selling Price (SP): This is the price at which an item is sold.
- Profit: Occurs when SP > CP. The profit amount is SP - CP.
- Loss: Occurs when SP < CP. The loss amount is CP - SP.
- Percentage calculations: Both profit and loss percentages are typically calculated with respect to the Cost Price unless specified otherwise. Understanding how to work with percentages in these formulas is crucial for solving such problems.
This problem combined both a loss scenario and a profit scenario, requiring us to first find the common link (Cost Price) before calculating the desired outcome.
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?
