Fan List Price Calculation: Markup, Discount, Profit

This solution explains how to find the list price of a fan given details about its cost price, markup percentage, discount percentage, and the final profit.

Understanding Price Components

• Cost Price (CP): The original price the shopkeeper paid for the fan.
• List Price (LP): The marked price before any discount is applied. Calculated as CP + 50% markup.
• Discount: A reduction of 10% applied to the List Price.
• Selling Price (SP): The final price after the discount ($LP - \text{Discount}$).
• Profit: The amount earned, calculated as $SP - CP$. Given as ₹56.

Step-by-Step Calculation Guide

1. Represent Variables:

   • Let $C$ represent the Cost Price.
   • Let $L$ represent the List Price.
   • Let $S$ represent the Selling Price.

2. Determine List Price (L):

   The list price is 50% above the cost price ($C$).

   Formula: $L = C + (\text{Markup Percentage} \times C)$

   $L = C + (50\% \times C)$

   $L = C + \frac{50}{100} \times C$

   $L = C + 0.50 C$

   $L = 1.50 C$

3. Calculate Selling Price (S):

   A 10% discount is given on the list price ($L$).

   Discount Amount = $10\% \times L = \frac{10}{100} \times L = 0.10 L$

   The Selling Price is the List Price minus the Discount:

   $S = L - \text{Discount Amount}$

   $S = L - 0.10 L$

   $S = 0.90 L$

   Substitute the expression for $L$ from Step 2 ($L = 1.50 C$):

   $S = 0.90 \times (1.50 C)$

   $S = 1.35 C$

4. Calculate Profit:

   Profit is the difference between the Selling Price ($S$) and the Cost Price ($C$).

   Profit = $S - C$

   Profit = $(1.35 C) - C$

   Profit = $0.35 C$

5. Find Cost Price (C):

   We are given that the profit is ₹56.

   Using the profit formula from Step 4:

   $0.35 C = 56$

   To find $C$, divide 56 by 0.35:

   $C = \frac{56}{0.35}$

   $C = \frac{5600}{35}$

   $C = 160$

   The Cost Price of the fan is ₹160.

6. Find List Price (L):

   The question asks for the List Price ($L$). Use the relationship from Step 2: $L = 1.50 C$.

   $L = 1.50 \times 160$

   $L = 240$

Final List Price Result

The list price of the fan is ₹240.