a retailer buys an article at a discount of 15% on printed price from a wholesaler. He makes up the price by 10%. Due to competition in the market, he allows a discount of 5% to buyer. If the buyer pays rupees 451.44 for the article inclusive of sale tax at 8% then find the profit percentage of retailer and the printed price of an article
To find the profit percentage of the retailer and the printed price of the article, we can work backward using the given information and the formula to calculate profit percentage.
Step 1: Calculate the selling price of the article.
The buyer paid Rs 451.44 inclusive of a sales tax of 8%. To find the selling price before the sales tax was added, we need to reverse the 8% sales tax.
Selling price after tax = Rs 451.44
Sales tax rate = 8%
Let's assume the selling price before tax is X.
X + 8% of X = Rs 451.44
Calculating the value of X:
1.08X = Rs 451.44
X = Rs 451.44 / 1.08
X ≈ Rs 418.00 (approx.)
So, the selling price of the article before sales tax was Rs 418.00.
Step 2: Calculate the price after the 5% discount given by the retailer.
The retailer allows a 5% discount to the buyer. To find the price after the discount, we need to reverse the 5% discount.
Price after discount = 95% of the selling price before tax.
Price after discount = 0.95 * Rs 418.00
Price after discount ≈ Rs 397.10 (approx.)
Step 3: Calculate the cost price of the article for the retailer after the 10% markup.
The retailer made up the price by 10%. To find the cost price for the retailer, we need to reverse the 10% markup.
Cost price = 90% of the price after discount.
Cost price = 0.90 * Rs 397.10
Cost price ≈ Rs 357.39 (approx.)
Step 4: Calculate the cost price of the article for the retailer, after the 15% discount from the wholesaler.
The retailer bought the article at a discount of 15% on the printed price. To find the cost price for the retailer after the discount, we need to reverse the 15% discount.
Cost price = 85% of the printed price.
Cost price = 0.85 * Printed price = Rs 357.39
Solving the equation:
0.85 * Printed price = Rs 357.39
Printed price ≈ Rs 420.46 (approx.)
So, the printed price of the article is approximately Rs 420.46.
Step 5: Calculate the profit percentage of the retailer.
Profit = Selling price - Cost price
Profit = Rs 418.00 - Rs 357.39 = Rs 60.61
Profit percentage = (Profit / Cost price) * 100
Profit percentage = (60.61 / 357.39) * 100 ≈ 17% (approx.)
Therefore, the profit percentage of the retailer is approximately 17%.
To find the profit percentage of the retailer, we need to determine the cost price of the article and the selling price.
Let's assume the printed price of the article is "P".
Given:
Discount received by the retailer from the wholesaler = 15% of P
Markup by the retailer = 10% of the price after the discount
So, the cost price (CP) for the retailer can be calculated as follows:
CP = P - Discount received from the wholesaler
CP = P - (15/100) * P
CP = (85/100) * P
The selling price (SP) after the markup can be calculated as follows:
SP = CP + Markup by the retailer
SP = (85/100) * P + (10/100) * (85/100) * P
SP = (85/100) * P + (85/100) * P/10
SP = (85/100) * P + (17/200) * P
SP = (85/100 + 17/200) * P
SP = (170 + 17)/200 * P
SP = (187/200) * P
Now, let's consider the discount given to the buyer. The selling price after the discount can be calculated as follows:
Selling price after discount = SP - Discount given to the buyer
Selling price after discount = (187/200) * P - (5/100) * (187/200) * P
Selling price after discount = (187/200) * P - (5/100) * (187/200) * P
Selling price after discount = (187/200) * P - (187/2000) * P
Selling price after discount = (187/200) * P - (187/2000) * P
Selling price after discount = (375 * P - 187 * P)/(400 * P)
Selling price after discount = (188/400) * P
Selling price after discount = (47/100) * P
We are given that the selling price after tax is Rs 451.44, inclusive of a 8% sales tax.
(47/100) * P + (8/100) * (47/100) * P = 451.44
By solving this equation, we can find the value of P (the printed price).
After finding P, we can calculate the profit percentage of the retailer using the formula:
Profit Percentage = (Profit / Cost Price) * 100
Where Profit = Selling Price - Cost Price.
Let's solve the equation to find the printed price "P" and calculate the profit percentage.
wholesaler's printed price: p
retailer's cost: 0.85p
price after markup: 0.85p*1.10 = 0.935p
price after buyer discount: 0.935p * 0.95 = 0.88825p
buyer pays .88825p*1.08 = 451.44
So, p = 470.59
price/cost for retailer is
.88825p/.85p = 1.045
so he made 4.5%