The list price of a air conditioner is ₹75000. It is sold to a retailer after two successive discounts of 2% and 30%. The retailer wants to earn a profit of 42% on his cost after allowing a 29% discount (on its new list price) to the customer. At what price should he list the air conditioner?

Given:

Original list price = ₹75000

Successive discounts = 2% and 30%

Retailer's desired profit = 42%

Customer discount on new list price = 29%

Formula used:

Successive Discount: Net% = a + b - (ab/100)

Profit% = (Selling Price - Cost Price)/Cost Price × 100

Calculation:

Cost to retailer:

⇒ After 2%: 75000 × 98/100 = 73500

⇒ After 30%: 73500 × 70/100 = 51450

Retailer wants 42% profit:

Let new list price = x

Selling price to customer = x × (100 - 29)% = x × 71/100

⇒ x × 71/100 = 51450 × (100 + 42)% = 51450 × 142/100

⇒ x × 71/100 = 73059

⇒ x = (73059 × 100) / 71

⇒ x = 102900

∴ New list price = ₹102900