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.