How do you find selling price when loss percentage and cost price is given?

A trademan sold an article at a loss of 20%. If the selling price had been increased by $100, there would have been gain of 5%. What was the cost price of the article ?

Solution :

Let x be the cost price of an article.

Cost price when loss happened  =  80% of x

  =  80x/100

  =  4x/5

Cost price when profit happened  =  105% of x

  =  105x/100

  =  21x/20

The difference between two cost prices  =  100

(21x/20) - (4x/5)  =  100

(21x-16x)/20  =  100

5x  =  100(20)

x  =  400 

Hence the required cost price is 400.

Example 3 :

A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for $1050 less, he would have gained 30%. How do I find the cost price of the article?

Solution :

Let x be the cost price of the article.

After 25% profit made, the selling price will be 125% of x.

Selling price  =  125x/100

Profit earned is 30% when the selling price be 1050 lesser than the previous price.

New selling price of the article  =  125x/100 - 1050

If cost price of article 20% less, then cost price  =  80% of x

Profit%  =  (Selling price - Cost price)/Cost price

30%  =  {[1.25x - 1050] - 0.80x}/0.8x

30(0.8x)  =  (1.25x - 1050 - 0.80x)

 0.24x =  0.45x - 1050

1050  =  0.45x - 0.24x

0.21x  =  1050

x  =  1050/0.21

x  =  5000

Hence the cost price of the article is $5000.

Example 4 :

A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for rupees 36.75 an less he would have gained 30%. Find the cost price of article.

Solution :

Let x be the cost price of the article.

After 25% profit made, the selling price will be 125% of x.

Selling price  =  125x/100

Profit earned is 30% when the selling price be 1050 lesser than the previous price.

New selling price of the article  =  125x/100 - 36.75

If cost price of article 20% less, then cost price  =  80% of x

Profit%  =  (Selling price - Cost price)/Cost price

30%  =  {[1.25x - 36.75] - 0.80x}/0.8x

0.3(0.8x)  =  (1.25x - 36.75 - 0.80x)

 0.24x =  0.45x - 36.75

36.75  =  0.45x - 0.24x

0.21x  =  36.75

x  =  36.75/0.21

x  =  175

Hence the cost price of the article is $175.

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We experience different situations every day when we need to calculate or compare things. Especially situations involving the sale or purchase of goods. The selling price is used to sell the item at a certain cost and can be calculated using the selling price formula. The amount that the buyer pays to buy the product is called the selling price. The actual selling price is the price the buyer pays to buy a product or service. This is the price that is higher than the cost of goods and includes a profit percentage. If the seller wishes, they can also keep the selling price similar to the cost price, if the buyer does not wish to gain profit. Determining the selling price is a very sensitive issue because sales of a product are largely based on it. We can calculate the selling price in various ways and formulas. 

The Basic Formula

SP = CP + Profit

Where,

SP= Selling Price

CP= Cost Price

This chapter deals with selling price and its role in calculating the percentage of profit and loss. We also learn the difference between selling price and marked price. We also learn how to calculate the selling price of a product using different formulas. There are various examples that will help us understand better about the selling price of an object. 

Important Selling Price Formula

1. Selling price = Cost Price + Profit

2. Selling price = Marked/List price – Discount

3. Selling price = (100+%Profit)/100 × Cost price

4. Selling price = (100− % Los)/100 × Cost price

Other Important Formulas Related To Selling Price

Element

Formula

Cost price

Selling price – Profit

Profit

Selling price – Cost Price

Loss

Cost Price – Selling Price

% Profit

Profit/Cost Price × 100

% Loss

Loss/Cost Price × 100

Marked price also known as the list price is the price that a seller spells out to the purchaser while selling price is the price that the seller actually receives from the buyer after a bargain or making a deal. In general, the selling price is lower than the marked price. However, sometimes the selling price and the marked price can be the same also. A fixed price shop, meaning that the shopkeeper that does not offer any discount or price cut of any sort is an example of it.

Calculate Selling Price Per Unit

Following is the step-by-step procedure to calculate the selling price per unit:

• Identify the total cost of all units being bought

•  Divide the total cost by the number of units bought to obtain the cost price.

• Use the selling price formula to find out the final price i.e.: SP = CP + Profit Margin

• Margin will then be added to the cost of the commodity in order to identify the appropriate pricing.

Thus, the selling price per unit formula to find the price per unit from the income statement, divide sales by the number of units or quantity sold to identify the price per unit.

For example, given sales of $80,000 for the year and 2,000 units sold, the price per unit is Rs.40 (80,000 divided by 2,000).

How to Calculate Cost-Plus Pricing

Markup is the amount of difference between an item’s cost and its selling price. Usually, depending on the industry type, it is demonstrated as a percentage of the cost.

Margin also referred to as Gross Profit) = Selling price – Cost of goods sold (COGS).

Margin and Markup move in tandem. For example, a 40% markup is always equivalent to a profit margin of 28.6%, while a 50% markup is always equivalent to a margin value of 33%.

Cost Price

Cost price is actually the ultimate price at which the seller buys the product or service. He then adds a percentage of profit to it. The list price or marked price is the price which a seller fixes after adding the needed percentage of profit.

Solved Examples

Example: Maria marks all her products 30% above the cost price and offers a discount of 5% on the marked price. She is of the viewpoint that she will earn a profit of 20%. What do you think is the percentage of the profit she earns?

Solution:

Let the cost price of the products be 100.

Thus, the list price/marked price will be = ₹100 + 30% of the cost price.

= 100 + 30

= 130

Now, the Selling price = List/Marked price – Discount

= 130 – 5% of 130 = 130 – 6.5

= 123.5

Therefore, the profit = SP-CP

= 123.5 – 100 = 23.5

Hence, the percentage of profit she earned is below 20%.

Example: A new retailer in the market marked all his goods at 50% above the cost price thinking that he will still earn a profit percent of 25%, offering a discount of 25% on the list price. Find out his actual profit on the sales?