Calculating the List Price of the Fan

This problem involves calculating the list price of a fan based on its cost price, a markup percentage, a discount percentage, and the final profit earned. Let's break down the steps:

Step-by-Step Calculation

1. Define Variables and Relationships

• Let the Cost Price (CP) of the fan be denoted by '$C$'.
• The shopkeeper lists the price (List Price, LP) at 60% above the cost price.
• The formula for List Price is:

  $ LP = CP + (60\% \text{ of } CP) $

  $ LP = C + \frac{60}{100} \times C $

  $ LP = C + 0.60C $

  $ LP = 1.60C $

• The shopkeeper offers a 15% discount on the List Price to determine the Selling Price (SP).
• The formula for Selling Price is:

  $ SP = LP - (15\% \text{ of } LP) $

  $ SP = LP - \frac{15}{100} \times LP $

  $ SP = LP \times (1 - 0.15) $

  $ SP = 0.85 \times LP $

• The Profit earned is the Selling Price minus the Cost Price. Profit = $SP - C$.
• We are given that the profit is ₹117.

2. Express Selling Price in terms of Cost Price

Substitute the expression for LP ($LP = 1.60C$) into the SP formula:

$ SP = 0.85 \times (1.60C) $

$ SP = 1.36C $

3. Calculate the Cost Price (CP)

Now use the profit information:

Profit = $SP - C$

₹117 = $1.36C - C$

₹117 = $0.36C$

To find C, divide the profit by 0.36:

$ C = \frac{117}{0.36} $

To simplify the division, multiply the numerator and denominator by 100:

$ C = \frac{11700}{36} $

Performing the division:

$ C = 325 $

So, the Cost Price (CP) of the fan is ₹325.

4. Calculate the List Price (LP)

Now that we have the Cost Price, we can find the List Price using the relationship $LP = 1.60C$:

$ LP = 1.60 \times 325 $

$ LP = \frac{160}{100} \times 325 $

$ LP = \frac{8}{5} \times 325 $

$ LP = 8 \times \frac{325}{5} $

$ LP = 8 \times 65 $

$ LP = 520 $

Therefore, the List Price of the fan is ₹520.

Summary Table