The marked price of mustard oil is 25% more than its cost price. At what percentage less than the marked price should it be sold to have no profit and no loss?
20%
Calculating Discount Percentage for No Profit No Loss
The question asks about finding the percentage discount needed on the marked price of mustard oil so that there is no profit or loss when sold. This means the selling price must be equal to the cost price.
We are given that the marked price is 25% more than the cost price. Let's assume a value for the cost price to make the calculation easier.
Step 1: Assume a Cost Price (CP)
Let the Cost Price (CP) of the mustard oil be $\text{Rs } 100$.
Step 2: Calculate the Marked Price (MP)
The marked price is 25% more than the cost price.
Increase in price = 25% of CP
Increase in price $= \frac{25}{100} \times 100 = \text{Rs } 25$
Marked Price (MP) = CP + Increase in price
MP $= 100 + 25 = \text{Rs } 125$
Step 3: Determine the Selling Price (SP) for No Profit No Loss
For a transaction to have no profit and no loss, the selling price must be equal to the cost price.
Selling Price (SP) = Cost Price (CP)
SP $= \text{Rs } 100$
Step 4: Calculate the Discount Amount
The discount is the difference between the marked price and the selling price.
Discount Amount = Marked Price (MP) - Selling Price (SP)
Discount Amount $= 125 - 100 = \text{Rs } 25$
Step 5: Calculate the Discount Percentage on Marked Price
The discount percentage is always calculated on the marked price unless otherwise specified.
Discount Percentage $= \left( \frac{\text{Discount Amount}}{\text{Marked Price}} \right) \times 100\%$
Discount Percentage $= \left( \frac{25}{125} \right) \times 100\%$
Discount Percentage $= \left( \frac{1}{5} \right) \times 100\%$
Discount Percentage $= 20\%$
So, the mustard oil should be sold at 20% less than the marked price to have no profit and no loss.
Let's summarise the values we found:
| Concept | Value (assuming CP = Rs 100) |
|---|---|
| Cost Price (CP) | Rs 100 |
| Marked Price (MP) | Rs 125 |
| Selling Price (SP) for No Profit/Loss | Rs 100 |
| Discount Amount | Rs 25 |
| Discount Percentage on MP | 20% |
Revision Table: Key Terms in Profit and Loss
| Term | Description | Relationship |
|---|---|---|
| Cost Price (CP) | The price at which an item is bought. | Basis for calculating profit/loss. |
| Marked Price (MP) | The price listed on the tag; often higher than CP. | Basis for calculating discount. |
| Selling Price (SP) | The price at which an item is sold. | Determines profit or loss (SP - CP). |
| Profit | When SP > CP. | Profit = SP - CP |
| Loss | When SP < CP. | Loss = CP - SP |
| Discount | Reduction offered on MP. | Discount = MP - SP |
| No Profit, No Loss | When SP = CP. | Profit = 0, Loss = 0 |
Additional Information: Profit, Loss, and Discount Concepts
- Profit Percentage: Calculated on CP. $\text{Profit \%} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\%$.
- Loss Percentage: Calculated on CP. $\text{Loss \%} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\%$.
- Discount Percentage: Calculated on MP. $\text{Discount \%} = \left( \frac{\text{Discount}}{\text{MP}} \right) \times 100\%$.
- In problems involving marked price and selling price, the relationship is often: $\text{SP} = \text{MP} \times \left( \frac{100 - \text{Discount \%}}{100} \right)$.
- When there is 'no profit, no loss', it simply means the selling price is exactly equal to the cost price.
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