A shopkeeper buys a blanket at a discount of 20% on the listed price from a wholesaler. The shopkeeper marks up the price by 15% on the listed price. A buyer pays Rs. 3795 to get it after paying sales tax rate of 10% on the price asked for. Find the profi

A shopkeeper buys a blanket at a discount of 20% on the listed price from a wholesaler. The shopkeeper marks up the price by 15% on the listed price. A buyer pays Rs. 3795 to get it after paying sales tax rate of 10% on the price asked for. Find the profit percentage of the shopkeeper.
1). 48.75%
2). 42.75%
3). 40.75%
4). 33.75%

Let the listed price of the blanket be $ x $.

The shopkeeper buys it at a discount of $20\%$ on the listed price, so the cost price (CP) for the shopkeeper is:

$ \text{CP} = x - \frac{20}{100}x = 0.8x $

The shopkeeper marks up the price by $15\%$ on the listed price, so the marked price (MP) is:

$ \text{MP} = x + \frac{15}{100}x = 1.15x $

The buyer pays Rs. 3795 after a sales tax of $10\%$ on the asked price.
Let the asked price (SP) be $ y $.

Since the buyer pays $10\%$ tax on $ y $, the total amount paid by the buyer is:

$ 1.1y = 3795 $

Solving for $ y $:

$ y = \frac{3795}{1.1} = 3450 $

Since the shopkeeper marks the price as $1.15x$, we assume no further discounts, so:

$ y = 1.15x $

Solving for $ x $:

$ x = \frac{3450}{1.15} = 3000 $

Now, calculating the cost price (CP):

$ \text{CP} = 0.8 \times 3000 = 2400 $

Profit earned by the shopkeeper:

$ \text{Profit} = \text{SP} - \text{CP} = 3450 - 2400 = 1050 $

Profit percentage:

$ \frac{1050}{2400} \times 100 = 43.75\% $

Thus, the shopkeeper's profit percentage is:

$ \boxed{43.75\%} $

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