A shopkeeper lists the price of a fan at 22% above its cost price and offers a 15% discount on its list price. What is the cost price (in Rs. ) of the fan if he sells it at Rs. 5,185? 

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  1. 5000
  2. 4500
  3. 4800
  4. 5680

Answer (Detailed Solution Below)

Option 1 : 5000
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Detailed Solution

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Given:

List price of the fan = 22% above cost price

Discount on list price = 15%

Selling price = Rs. 5,185

Formula Used:

List Price (LP) = Cost Price (CP) + 22% of CP

Selling Price (SP) = LP - 15% of LP

Calculation:

Let the cost price of the fan be Rs. x.

List Price (LP) = x + 0.22x

⇒ LP = 1.22x

After a 15% discount, the selling price is:

Selling Price (SP) = LP - 0.15LP

⇒ SP = 1.22x - 0.15(1.22x)

⇒ SP = 1.22x × (1 - 0.15)

⇒ SP = 1.22x × 0.85

Given that the selling price is Rs. 5,185:

5,185 = 1.22x × 0.85

⇒ 5,185 = 1.037x

⇒ x = 5,185 / 1.037

⇒ x = 5,000

The cost price of the fan is Rs. 5,000.

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