Dipali bought a set of cups for Rs. 375, but then had to sell it later to clear old stocks for Rs. 345. What is the percentage of loss that she incurred?
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Calculating Percentage Loss on Sale
Let's break down how to calculate the percentage of loss Dipali incurred when selling the set of cups.
Understanding Cost Price and Selling Price
- Cost Price (CP): This is the original price at which Dipali bought the set of cups. In this case, CP = Rs. 375.
- Selling Price (SP): This is the price at which Dipali sold the set of cups. Here, SP = Rs. 345.
Identifying Loss or Profit
When the Selling Price is less than the Cost Price, it is a case of loss. If the Selling Price is greater than the Cost Price, it is a profit.
In this problem, SP (Rs. 345) < CP (Rs. 375), so Dipali incurred a loss.
Calculating the Amount of Loss
The amount of loss is the difference between the Cost Price and the Selling Price.
Loss = Cost Price - Selling Price
Loss = Rs. 375 - Rs. 345
Loss = Rs. 30
Dipali incurred a loss of Rs. 30.
Calculating the Percentage Loss
Percentage loss is calculated with respect to the Cost Price. The formula for percentage loss is:
\(\text{Percentage Loss} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100\%\)
Now, let's plug in the values:
\(\text{Percentage Loss} = \left( \frac{30}{375} \right) \times 100\%\)
To simplify the fraction \(\frac{30}{375}\):
- Both 30 and 375 are divisible by 5: \(\frac{30 \div 5}{375 \div 5} = \frac{6}{75}\)
- Both 6 and 75 are divisible by 3: \(\frac{6 \div 3}{75 \div 3} = \frac{2}{25}\)
So, the percentage loss calculation becomes:
\(\text{Percentage Loss} = \left( \frac{2}{25} \right) \times 100\%\)
\(\text{Percentage Loss} = \frac{2 \times 100}{25}\%\)
\(\text{Percentage Loss} = 2 \times \frac{100}{25}\%\)
\(\text{Percentage Loss} = 2 \times 4\%\)
\(\text{Percentage Loss} = 8\%\)
The percentage of loss Dipali incurred is 8%.
Revision Table: Profit and Loss Basics
| Concept | Formula | Condition |
|---|---|---|
| Loss | CP - SP | SP < CP |
| Profit | SP - CP | SP > CP |
| Percentage Loss | \(\left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\%\) | When there is a loss |
| Percentage Profit | \(\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\%\) | When there is a profit |
Additional Information on Loss and Profit
Understanding loss and profit is fundamental in business and everyday finance. Here are a few key points:
- Loss and profit are always calculated based on the Cost Price unless otherwise specified.
- A loss occurs when the money received from selling something is less than the money spent to acquire it.
- A profit occurs when the money received from selling something is more than the money spent to acquire it.
- Knowing how to calculate percentage loss or profit helps in comparing the performance of different sales or investments.
- In this scenario, Dipali had to sell the cups at a loss, possibly due to clearing old stocks, as mentioned in the question. Businesses sometimes do this to free up space or capital, even if it means a loss on specific items.
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