Mohit purchased a table for Rs. 1,260 and due to some scratches on its top, he sold it for Rs. 1,197. What is his loss percent?
5%
Calculating Loss Percent on a Table Purchase
The problem asks us to find the loss percent incurred by Mohit when he purchased a table and then sold it for a lower price due to scratches.
First, let's identify the key values given in the question:
- Cost Price (CP) of the table = Rs. 1,260
- Selling Price (SP) of the table = Rs. 1,197
Since the Selling Price is less than the Cost Price, there is a loss in this transaction.
The formula to calculate the Loss is:
\( \text{Loss} = \text{Cost Price} - \text{Selling Price} \)
Let's calculate the amount of loss:
\( \text{Loss} = 1260 - 1197 \)
\( \text{Loss} = 63 \)
So, Mohit incurred a loss of Rs. 63.
Next, we need to calculate the Loss Percent. The formula for Loss Percent is:
\( \text{Loss Percent} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 \)
Now, let's substitute the values into the formula:
\( \text{Loss Percent} = \left( \frac{63}{1260} \right) \times 100 \)
We can simplify the fraction \( \frac{63}{1260} \). Both 63 and 1260 are divisible by 63 (since 126 is \( 2 \times 63 \), 1260 is \( 20 \times 63 \)).
\( \frac{63}{1260} = \frac{1}{20} \)
Now, substitute this simplified fraction back into the Loss Percent formula:
\( \text{Loss Percent} = \left( \frac{1}{20} \right) \times 100 \)
\( \text{Loss Percent} = \frac{100}{20} \)
\( \text{Loss Percent} = 5 \)
Therefore, the loss percent is 5%.
Let's verify the steps and the result.
| Item | Value | Notes |
|---|---|---|
| Cost Price (CP) | Rs. 1,260 | Original price paid |
| Selling Price (SP) | Rs. 1,197 | Price sold for |
| Loss | Rs. 63 | CP > SP, so there is a loss |
| Loss Percent | 5% | Calculated based on CP |
The calculation confirms that the loss percent is 5%.
Revision Table: Key Concepts for Loss Percent Calculation
| Term | Definition | Formula |
|---|---|---|
| Cost Price (CP) | The price at which an item is bought. | N/A |
| Selling Price (SP) | The price at which an item is sold. | N/A |
| Loss | Occurs when SP < CP. | \( \text{Loss} = \text{CP} - \text{SP} \) |
| Loss Percent | Loss expressed as a percentage of the Cost Price. | \( \text{Loss Percent} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \) |
Additional Information on Profit and Loss
Understanding profit and loss is fundamental in commercial arithmetic. These concepts help in determining the financial outcome of a transaction.
- Profit: A profit occurs when the Selling Price (SP) is greater than the Cost Price (CP). The profit amount is calculated as \( \text{Profit} = \text{SP} - \text{CP} \).
- Profit Percent: When there is a profit, the profit percent is calculated based on the Cost Price using the formula \( \text{Profit Percent} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \).
- Loss: As seen in this problem, a loss occurs when the Selling Price (SP) is less than the Cost Price (CP). The loss amount is \( \text{Loss} = \text{CP} - \text{SP} \).
- Loss Percent: The loss percent is calculated based on the Cost Price using the formula \( \text{Loss Percent} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \).
It is important to note that both profit percent and loss percent are always calculated with respect to the Cost Price, unless stated otherwise.
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