The list price of a washing machine is ₹41000. It is sold to a retailer after two successive discounts of 12% and 30%. The retailer wants to earn a profit of 25% on it's cost price after allowing a 50% discount (on its new list price) to the customer. At what price should he list the washing machine?

Correct option is A

Given:

The list price of the washing machine is ₹41,000.

Successive discounts of 12% and 30% are applied to the washing machine's price when sold to the retailer.

The retailer wants to earn a profit of 25% on the cost price after offering a 50% discount on the new list price to the customer.

Solution:

The price after the first discount is calculated as: 

Price after first discount = 41,000 × (1 − 0.12) = 41,000 × 0.88 = 36,080

The price after the second discount is: 

Price after second discount = 36,080 × (1 − 0.30) = 36,080 × 0.70 = 25,256 

Thus, the cost price for the retailer is ₹25,256.

Let the list price that the retailer sets be $P$.

So the selling price to the customer will be:

​$$\text{Selling price to customer} = \frac{P}{2}$$ 

So the desired selling price (before discount) should be:

Desired selling price = 25,256 × (1 + 0.25) = 25,256 × 1.25 = 31,570

Thus, the price at which the retailer wants to sell before discount should be ₹31,570.

The price at which the retailer sells to the customer after applying the 50% discount is half of the list price. This should equal the desired selling price of ₹31,570.

​$$\frac{P}{2} = 31,570$$​​

P = 31,570 × 2 = 63,140  

The retailer should list the washing machine at ₹63,140.​