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?
846.40
Calculating Selling Price with Loss and Gain Percentage
This problem involves calculating the cost price of an article based on a given selling price and a percentage loss on the selling price, and then finding the new selling price required to achieve a specific percentage gain on the cost price.
Step 1: Understanding the Initial Loss Condition
We are told that when the article is sold for Rs. 640, the person loses 15% of its selling price.
- Selling Price (SP) = Rs. 640
- Loss Percentage is 15% of the Selling Price.
Step 2: Calculating the Loss Amount
The loss amount is 15% of the selling price (Rs. 640).
Loss Amount $$ = 15\% \text{ of } 640 $$
Loss Amount $$ = \frac{15}{100} \times 640 $$
Loss Amount $$ = \frac{3}{20} \times 640 $$
Loss Amount $$ = 3 \times 32 $$
Loss Amount $$ = \text{Rs. } 96 $$
Step 3: Calculating the Cost Price
When there is a loss, the Cost Price is the Selling Price plus the Loss Amount.
Cost Price (CP) $$ = \text{Selling Price} + \text{Loss Amount} $$
CP $$ = 640 + 96 $$
CP $$ = \text{Rs. } 736 $$
So, the original cost price of the article is Rs. 736.
Step 4: Understanding the Target Gain Condition
Now, we want to find the price at which the article should be sold to gain 15% on its cost price.
- Cost Price (CP) = Rs. 736
- Target Gain Percentage is 15% of the Cost Price.
Step 5: Calculating the Required Gain Amount
The required gain amount is 15% of the cost price (Rs. 736).
Gain Amount $$ = 15\% \text{ of } 736 $$
Gain Amount $$ = \frac{15}{100} \times 736 $$
Gain Amount $$ = \frac{3}{20} \times 736 $$
Gain Amount $$ = \frac{2208}{20} $$
Gain Amount $$ = 110.40 $$
Gain Amount $$ = \text{Rs. } 110.40 $$
Step 6: Calculating the Target Selling Price
To find the selling price needed to achieve the gain, we add the Gain Amount to the Cost Price.
Target Selling Price $$ = \text{Cost Price} + \text{Gain Amount} $$
Target Selling Price $$ = 736 + 110.40 $$
Target Selling Price $$ = \text{Rs. } 846.40 $$
Therefore, the person should sell the article for Rs. 846.40 to gain 15% on its cost price.
| Scenario | Selling Price (SP) | Cost Price (CP) | Loss/Gain Basis | Loss/Gain Percentage | Loss/Gain Amount | Relationship |
|---|---|---|---|---|---|---|
| Initial Loss | Rs. 640 | ? | Selling Price | 15% | Rs. 96 | CP = SP + Loss |
| Target Gain | ? | Rs. 736 | Cost Price | 15% | Rs. 110.40 | Target SP = CP + Gain |
Revision Table: Key Concepts
| Concept | Formula (Loss on SP) | Formula (Gain on CP) |
|---|---|---|
| Loss Amount | Loss % of SP | N/A |
| Gain Amount | N/A | Gain % of CP |
| Cost Price (with Loss on SP) | SP + Loss Amount | N/A |
| Selling Price (with Gain on CP) | N/A | CP + Gain Amount |
Additional Information: Profit and Loss Basics
Profit and loss calculations are fundamental concepts in commercial arithmetic. It's important to note whether the percentage is calculated on the Cost Price (CP) or the Selling Price (SP), as this significantly affects the calculations.
- Cost Price (CP): The price at which an article is bought.
- Selling Price (SP): The price at which an article is sold.
- Profit: When SP > CP. Profit = SP - CP. Profit % is usually calculated on CP unless specified otherwise: Profit % = (Profit / CP) * 100.
- Loss: When SP < CP. Loss = CP - SP. Loss % is usually calculated on CP unless specified otherwise: Loss % = (Loss / CP) * 100.
In this specific problem, the initial loss was stated to be on the Selling Price, which is a less common scenario but clearly defined in the question.
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