Cost price is the price at which an article is bought. All the expenditures that are made over the actual cost are included in the cost price of that article. Profit and loss measurement is generally done in terms of cost price. When articles are traded, the cost at which they are vended is known as the selling price of that article. In maths we may face different types of problems based on evaluating profits and losses using the cost price and selling price of the articles. Let us consider an example of such problems to understand them better:
Example: If selling price 55 and cost price 50 than how much profit in rupees and Percentage?
Solution: According to the question we have been given the cost price equals to 50 and the selling or vending price of article as 55. The profit seems to occur when vending price is more as compared to the cost or actual price of the article and loss prevails in the conditions where the selling price is less as compared to actual (market) price of the article.
Here in our example we are actually gaining profit in selling the good.
Formula for evaluating the profit is given as follows:
Profit (Rupees) = Vending Price – Market Price (Cost Price),
Profit (Percentage) = ((Vending Price – Market Price (Cost Price)) / Cost Price) * 100,
Here, Vending Price = 55 and Cost Price = 50,
Substituting the values of both in the above formula we get:
Profit (Rupees) = 55 – 50 = Rs. 5
Evaluating the equivalent percentage profit:
Profit (%) = 5 / 50 * 100,
Or Profit (%) = 100 / 10 = 10 %,
So, amount of profit earned by the person is 10 % or Rs. 5.
Math word problems may also include solving discounts on original prices. Discount is a quantity that can either be represented in simple currency form or in Percentage form. When it is represented in currency form, we just have to perform the deductions of it with any further calculation. But same is not the case with percentage values. To convert a percentage to Ratio we divide the percentage value by 100 and to calculate the discounted value we need to perform further operations. Such word problems can be understood by considering following example:
Let us suppose word problem which says: After a 15 percent discount on TV it now cost 102 dollars, what is the original price?
Solution: In a word problem what we actually look for in the beginning is the available information. Here in our example this information is present in the form of discounted price of the TV and the amount of discount made on the original price of it. Also we have important information about the units of money and discount. The discount has been specified in terms of percentage and the discounted price in dollars. Let us suppose that the original price of TV is X dollars. Applying a discount of 15 % on it and subtracting the value from X we get:
X - (15 % of X) = 102,
Or X - (15 / 100) * X = 102,
Or X (1 - (15 / 100)) = 102,
or X (85 / 100) = 102,
Multiplying both sides of the equation by (100 / 85) we get:
X (85 / 100) * (100 / 85)= 102 * (100 / 85),
X = 102 * (100 / 85),
or X = $ 120,
So, the original price of the Tv is $ 120.
In Math we may also find the word problems based on the cost price, selling price, profit, loss etc. Cost price of a good is the price at which it is bought and selling price is the price of good at which it is sold. Profit and loss can be calculated in terms of % or price value as follows:
Profit is calculated by subtracting Cost Price (CostP) from the Selling Price (SellP) of the good and Loss is calculated by subtracting Selling Price (SellP) from Cost Price (CostP) of good.
Profit % = ((SellP) – (CostP)) * (100 / (CostP)),
Loss % = ((CostP) – (SellP)) * (100 / (CostP)),
Let us now take an example of it to understand it better:
Q. By selling a good a person loses 15 percent of the sp find his actual loss?
Solution: To find the actual loss we would be using following formula:
(SellP) = (100 – LOSS %) * ((CostP) / 100),
Let selling price of good is $20,000 and according to the question 15 % loss is suffered by the person on selling price of the good. Substituting the values of given quantities in above formula we get value of cost price of good as follows:
20,000 = (100 – 15) * CostP / 100,
Or CostP = (20000 * 100) / 75,
Or CostP = 20000 * 4 / 3 = 80,000 / 3 = $ 27,000 approx.
Total loss suffered by the person can be calculated using the formula:
Loss = CostP – SellP,
Substituting the value of cost price and selling price of the good in the above equation we get:
Loss = $. 27000 - $ 20000 = $ 7000.