A retailer announces a discount of 30% for selling an air-conditioner marked at Rs. 92,000. The cost price of the air-conditioner is 70% below the marked price. He offers a further discount of 20% if the buyer presents his membership card of the retailer's store. The profit of the retailer with the membership card scheme is what percentage of the profit of the retailer without the membership card scheme?

Shortcut TrickWithout membership,

MP = 100 , CP = 30, SP = 70

Profit = 70 - 30 = 40

With membership,

MP = 100 , CP = 30

Total discount = 30 + 20 - 30×20/100 = 44%

SP = 100 - 44 = 56%

Profit = 56 - 30 = 26 

Required % = 26/40 × 100 = 65%

∴ The correct answer is 65%.

Given:

A retailer announces a discount of 30% for selling an air-conditioner marked at Rs. 92,000.

The cost price of the air-conditioner is 70% below the marked price.

He offers a further discount of 20% if the buyer presents his membership card of the retailer's store

Formula used:

Selling Price (Sp) = Cp + (\(\frac{Profit}{100}\)) × Cp

Cp = (\(\frac{100}{100\space+\space profit\space Percent}\)) × Sp

Calculation:

The selling price after giving 30% discount is

⇒ 92000 × 70/100 = Rs 64,400

The cost price is 92000 × 30/100 = Rs 27600

Now profit will be 64400 - 27600 = Rs 36800

If he gives additional 20% discount then price,

⇒  64,400 × 80/100 = Rs 51520

Then profit is 51520 - 27600 = Rs 23920

So required percentage is ,

⇒ (23920 / 36800) × 100 = 65%

∴ The correct option is 2

Additional Information 

Profit is calculated on Cost Price.

And the discount is calculated on Market Price.