Calculate Retailer's Cost Price (CP)

The initial list price is ₹15,000. Two successive discounts of 32% and 40% are applied to find the retailer's cost price.

• Price after the first discount (32%):

  $ ₹15,000 \times (1 - \frac{32}{100}) = ₹15,000 \times (1 - 0.32) = ₹15,000 \times 0.68 = ₹10,200 $

• Price after the second discount (40%):

  $ ₹10,200 \times (1 - \frac{40}{100}) = ₹10,200 \times (1 - 0.40) = ₹10,200 \times 0.60 = ₹6,120 $

So, the retailer's Cost Price (CP) is ₹6,120.

Calculate Retailer's Selling Price (SP)

The retailer wants a 45% profit on his cost price. The selling price is calculated as:

$ SP = CP \times (1 + \text{Profit Percentage}) $

$ SP = ₹6,120 \times (1 + \frac{45}{100}) $

$ SP = ₹6,120 \times (1 + 0.45) $

$ SP = ₹6,120 \times 1.45 $

$ SP = ₹8,874 $

The retailer needs to sell the refrigerator for ₹8,874 to achieve the desired profit.

Determine Retailer's List Price

The retailer allows a 49% discount on his list price to the customer. The selling price (SP) is 51% (100% - 49%) of the retailer's list price (LP).

$ SP = LP \times (1 - \text{Discount Percentage}) $

$ ₹8,874 = LP \times (1 - \frac{49}{100}) $

$ ₹8,874 = LP \times (1 - 0.49) $

$ ₹8,874 = LP \times 0.51 $

To find the list price (LP), we rearrange the formula:

$ LP = \frac{₹8,874}{0.51} $

$ LP = ₹17,400 $

Therefore, the retailer should list the refrigerator at ₹17,400.