Assume Cost Price

Let the cost price (CP) of the fan be $100x$.

$CP = 100x$

Determine List Price

The shopkeeper lists the price at 20% above the cost price.

$\text{List} \text{Price} (MP) = 120x$

Calculate Selling Price

A discount of 10% is offered on the list price. The selling price (SP) becomes $120x \times (1 - 0.10) = 108x$.

$SP = 108x$

Equate Profit and Solve for x

Profit is given as ₹150. Therefore, $SP - CP = 108x - 100x = 8x = 150$. Solving gives $x = \frac{150}{8} = 18.75$.

$8x = 150 \implies x = 18.75$

Calculate List Price

Substitute $x = 18.75$ into the list price expression: $120 \times 18.75 = 2250$.

$\text{List Price} = 120 \times 18.75 = \text{₹}2250$