A table was bought for Rs. 3,000 and sold for Rs. 3,200. Find the gain or loss in terms of money.
Gain Rs. 200
Calculating Gain or Loss on Selling a Table
This problem asks us to determine if there is a gain (profit) or a loss when an item is bought and then sold, and to find the amount of that gain or loss in terms of money.
Understanding Cost Price and Selling Price
- Cost Price (CP): This is the price at which an item is bought. In this case, the cost price of the table is Rs. 3,000.
- Selling Price (SP): This is the price at which an item is sold. Here, the selling price of the table is Rs. 3,200.
Determining Gain or Loss
We compare the Selling Price (SP) with the Cost Price (CP) to determine if there is a gain or a loss:
- If Selling Price (SP) > Cost Price (CP), there is a Gain.
- If Selling Price (SP) < Cost Price (CP), there is a Loss.
- If Selling Price (SP) = Cost Price (CP), there is neither gain nor loss.
In this problem:
- Cost Price (CP) = $\text{Rs. } 3,000$
- Selling Price (SP) = $\text{Rs. } 3,200$
Since $\text{Rs. } 3,200 > \text{Rs. } 3,000$, we have $\text{Selling Price (SP)} > \text{Cost Price (CP)}$. This means there is a Gain.
Calculating the Amount of Gain
The amount of gain is calculated by subtracting the Cost Price (CP) from the Selling Price (SP).
The formula for Gain is:
$\text{Gain} = \text{Selling Price (SP)} - \text{Cost Price (CP)}$
Now, let's substitute the given values into the formula:
$\text{Gain} = \text{Rs. } 3,200 - \text{Rs. } 3,000$
$\text{Gain} = \text{Rs. } 200$
So, the gain in terms of money is Rs. 200.
Final Answer Analysis
The calculation shows a gain of Rs. 200. Let's look at the options provided:
- Gain Rs. 200
- Loss Rs. 200
- Gain Rs. 100
- Loss Rs. 150
Our calculated gain of Rs. 200 matches option 1.
| Item | Value |
|---|---|
| Cost Price (CP) | Rs. 3,000 |
| Selling Price (SP) | Rs. 3,200 |
| Result | Gain |
| Gain Amount | Rs. 200 |
Revision Table: Gain and Loss Concepts
| Concept | Formula | Condition | Explanation |
|---|---|---|---|
| Gain (Profit) | $\text{Gain} = \text{SP} - \text{CP}$ | SP > CP | Money earned more than the cost. |
| Loss | $\text{Loss} = \text{CP} - \text{SP}$ | SP < CP | Money lost compared to the cost. |
| Neither Gain nor Loss | SP = CP | Sold at the same price as bought. |
Additional Information: Related Concepts in Profit and Loss
Beyond just the amount of gain or loss, we often calculate the percentage of gain or loss. This is done with respect to the Cost Price (CP).
- Gain Percentage ($\text{Gain } \%$): This tells us the gain as a percentage of the cost price.
- Formula: $\text{Gain } \% = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100$
- In this problem: $\text{Gain } \% = \left( \frac{200}{3000} \right) \times 100 = \left( \frac{1}{15} \right) \times 100 \approx 6.67\%$
- Loss Percentage ($\text{Loss } \%$): This tells us the loss as a percentage of the cost price.
- Formula: $\text{Loss } \% = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100$
- This is only applicable when there is a loss (SP < CP).
Understanding gain and loss is fundamental in business mathematics and everyday financial calculations.
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