To find the marked price (MP) of the oven, we need to work backward from the cost price (CP) using the given profit and discount information.
Oven Cost Price and Profit Calculation
The dealer purchased the oven for ₹54,000. This is the Cost Price (CP).
The dealer gains a profit of 75%. We can calculate the Selling Price (SP) using the formula:
$$ \text{SP} = \text{CP} \times (1 + \frac{\text{Profit Percentage}}{100}) $$
Substituting the values:
$$ \text{SP} = ₹54,000 \times (1 + \frac{75}{100}) $$
$$ \text{SP} = ₹54,000 \times (1 + 0.75) $$
$$ \text{SP} = ₹54,000 \times 1.75 $$
$$ \text{SP} = ₹94,500 $$
So, the selling price of the oven is ₹94,500.
Oven Selling Price and Marked Price Relation
The dealer allows a discount of 10% on the marked price (MP). The selling price (SP) is the marked price minus the discount.
The formula relating SP, MP, and Discount is:
$$ \text{SP} = \text{MP} \times (1 - \frac{\text{Discount Percentage}}{100}) $$
We know the SP is ₹94,500 and the discount is 10%.
$$ ₹94,500 = \text{MP} \times (1 - \frac{10}{100}) $$
$$ ₹94,500 = \text{MP} \times (1 - 0.10) $$
$$ ₹94,500 = \text{MP} \times 0.90 $$
Final Marked Price Calculation
To find the marked price (MP), we rearrange the formula:
$$ \text{MP} = \frac{\text{SP}}{0.90} $$
Substituting the calculated SP:
$$ \text{MP} = \frac{₹94,500}{0.90} $$
$$ \text{MP} = \frac{₹94,500}{9/10} $$
$$ \text{MP} = ₹94,500 \times \frac{10}{9} $$
$$ \text{MP} = ₹10,500 \times 10 $$
$$ \text{MP} = ₹105,000 $$
Therefore, the marked price of the oven is ₹105,000.
Important Questions from Profit and Loss
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
