The list price of a refrigerator is ₹15,000. It is sold to a retailer after two successive discounts of 32% and 40%. The retailer wants to earn a profit of 45% on his cost after allowing a 49% discount (on its new list price) to the customer.

At what price should he list the refrigerator?

The correct option is ₹17,400.

Let us break down the solution step-by-step to understand how this answer is derived.

Step 1: Calculate the cost price (CP) for the retailer.
The original list price of the refrigerator is ₹15,000.
The retailer buys it after two successive discounts of 32% and 40%.

First discount of 32% reduces the price to:
$$\mathrm{15,000}\times (1-0.32)=\mathrm{15,000}\times 0.68=\mathrm{10,200}$$
Second discount of 40% reduces this intermediate price to:
$$\mathrm{10,200}\times (1-0.40)=\mathrm{10,200}\times 0.60=\mathrm{6,120}$$
Thus, the cost price (CP) for the retailer is ₹6,120.

Step 2: Determine the required selling price (SP) to make a profit of 45%.
The retailer wants a profit of 45% on his cost price.
$$\text{SP}=\text{CP}\times (1+0.45)$$
$$\text{SP}=\mathrm{6,120}\times 1.45=\mathrm{8,874}$$
So, the selling price needs to be ₹8,874.

Step 3: Calculate the new list price (marked price, MP) for the customer.
The retailer wants to offer a 49% discount on this new list price while still obtaining the selling price of ₹8,874.
Let the new list price be MP.
$$\text{SP}=\text{MP}\times (1-0.49)$$
$$\mathrm{8,874}=\text{MP}\times 0.51$$
Solving for MP:
$$\text{MP}=\frac{\mathrm{8,874}}{0.51}=\mathrm{17,400}$$
Therefore, the retailer should list the refrigerator at ₹17,400.