A girl purchases 9 mangoes for Rs. 90 and sells 10 mangoes for Rs. 95. Find the gain or loss percentage.
5% loss
Understanding Profit and Loss Percentage
This problem involves calculating the gain or loss percentage when buying and selling a different number of items at different prices. To compare effectively, we need to find the cost price (CP) and selling price (SP) for a single unit of the item (in this case, a single mango).
Calculating Cost Price (CP) per Mango
The girl purchases 9 mangoes for Rs. 90. The cost price for 9 mangoes is Rs. 90.
To find the cost price of one mango, we divide the total cost by the number of mangoes:
CP per mango = Total Cost / Number of mangoes
CP per mango = Rs. 90 / 9
CP per mango = Rs. 10
So, the cost price of one mango is Rs. 10.
Calculating Selling Price (SP) per Mango
The girl sells 10 mangoes for Rs. 95. The selling price for 10 mangoes is Rs. 95.
To find the selling price of one mango, we divide the total selling price by the number of mangoes sold:
SP per mango = Total Selling Price / Number of mangoes sold
SP per mango = Rs. 95 / 10
SP per mango = Rs. 9.50
So, the selling price of one mango is Rs. 9.50.
Determining Gain or Loss
Now, we compare the cost price per mango and the selling price per mango:
- CP per mango = Rs. 10
- SP per mango = Rs. 9.50
Since the Selling Price (Rs. 9.50) is less than the Cost Price (Rs. 10), there is a loss in this transaction.
Calculating the Loss Amount
The loss per mango is the difference between the Cost Price and the Selling Price:
Loss per mango = CP per mango - SP per mango
Loss per mango = Rs. 10 - Rs. 9.50
Loss per mango = Rs. 0.50
The loss on selling one mango is Rs. 0.50.
Calculating Loss Percentage
The loss percentage is calculated based on the cost price. The formula for loss percentage is:
\(\text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\)
Using the values we calculated:
Loss = Rs. 0.50
CP per mango = Rs. 10
\(\text{Loss Percentage} = \left( \frac{0.50}{10} \right) \times 100\)
\(\text{Loss Percentage} = 0.05 \times 100\)
\(\text{Loss Percentage} = 5\%\)
The loss percentage is 5%.
Therefore, the girl incurs a loss of 5%.
Revision Table: Profit and Loss Key Concepts
| Concept | Formula | Condition |
|---|---|---|
| Cost Price (CP) | Original price of an item | - |
| Selling Price (SP) | Price at which item is sold | - |
| Profit | SP - CP | If SP > CP |
| Loss | CP - SP | If CP > SP |
| Profit Percentage | \(\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\) | Calculated on CP |
| Loss Percentage | \(\left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\) | Calculated on CP |
Additional Information on Profit and Loss Calculation
When dealing with profit and loss problems involving different quantities bought and sold, it's crucial to standardize the comparison. This can be done in two main ways:
- Calculate CP and SP per Unit: As shown in this solution, find the cost and selling price for a single item. This makes direct comparison easy.
- Calculate CP and SP for a Common Quantity: Find the least common multiple (LCM) of the number of items bought and sold. Then calculate the total CP and total SP for that common quantity. For example, in this problem, the LCM of 9 and 10 is 90. You could calculate the cost of 90 mangoes and the selling price of 90 mangoes to find the total gain or loss for that quantity.
Both methods should yield the same percentage gain or loss. The percentage is always calculated relative to the original cost price (CP).
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