A shopkeeper lists the price of a fan at 20% above its cost price and offers a 15% discount on its list price. If he earns aprofit of ₹190, then what is the list price (in ₹) of the fan?

Correct option is D

Given:

Profit earned = ₹190

The price of the fan is listed 20% above its cost price.

A 15% discount is offered on the list price.

Solution:

Let the cost price be CC.

The list price is 20% above the cost price: List Price = C + 0.20C = 1.20C

A 15% discount on the list price means the selling price is 85% of the list price:

Selling Price = 0.85 × List Price = 0.85 × 1.20C = 1.02C

Profit earned is the difference between the selling price and cost price:

Profit = Selling Price − Cost Price = 1.02C – C = 0.02C

Now,

C = $$\frac{190}{0.02}$$​ = ₹9500

List Price = 1.20 × 9500 = ₹11400

Therefore, the list price of the fan is ₹11400.

Alternate Method: ​

20% = $$\frac{1}{5}$$ So, CP = 5 and MP = 6 

Now, 15% is given on MP,  So, $$6 \times \frac{85}{100} = 5.1$$ 

Profit = 5.1 - 5 = 0.1 

0.1 = 190 then 1 = 1900 

So, 6 = 1900 × 6 = ₹11400