The topic of Profit and Loss is a straightforward application of Percentages. There is very little new matter that one would study.
In most of the problems, there would be a trader who sells goods to a customer. The price at which the trader sells the goods is called the Selling Price (SP, in short).
The trader would either be purchasing the good from else-where or manufacturing it. In either of the cases, he would be incurring a cost. This is called his Cost Price (CP, in short)
To find if the trade has resulted in a profit or loss, we would always consider the difference (SP CP). If the SP is greater than the CP, as usually is the case, the difference is positive and we say that the trader has earned a Profit. If the SP is less than the CP, the difference is negative and we say the trader has incurred a Loss. Profit or Loss = (SP CP), if positive, it is Profit, if negative it is Loss
Here’s a question for you A product has resulted in a profit, say of Rs. 1000, as compared to another product which results in a profit of Rs. 100. Which product has yielded a higher profit?
Solution: C. Can’t really say.
Whenever we have to compare two products, the absolute value of the profit is not of much use.While the first product may seem attractive because of the higher absolute value of profit if the first product costs Rs. 10,000 and the second product costs only Rs. 200, the scenario changes. Having spent Rs. 10,000 and making a profit of only 1,000 (1/10th of the investment) is not as lucrative as spending only Rs. 200 and making a profit of Rs. 100 (1/2 of the investment).
To compare two products, a better measure would be Profit/Cost Price. This figure is usually expressed in percentage terms i.e. profit per Rs. 100 of cost. This is termed as Profit Percentage. Thus, Profit Percentage = Profit/Cost Price 100%.Profit/Loss percentage is quite useful in solving Standard problems on Profit and Loss
1. A trader purchases a good at Rs. 500 and is forced to sell it at Rs. 450. Find his profit/loss percentage.
In this case, there is a loss i.e. Profit = 450 500 = 50. Profit percentage = -50/500 * 100 i.e., -1/10 * 100 = 10% loss
2. Amit sells his watch for Rs. 200 for a profit of 20%. At what price did Amit purchase the watch?
Please note that 20% is of the CP which is not known and it is NOT of 200. Thus CP + 20% of CP = 200This is the same as a 20% increase in CP results in 200. Thus using percentage increase funds learned in the earlier chapter, we have
3. Ramesh sells his watch for Rs. 100 and makes a loss of Rs. 10. Find the loss percentage.
These easy questions are given just to rub in the fact that the Profit or Loss percentage is always of CP and not SP. Thus in this question, 10 % loss is the wrong answer as 10 is found as a percentage of 100, which is the SP and not CP.CP = 100 + 10 = 110Loss percentage = 10/110 * 100 i.e., 1/11 or 9.0909%
Sometimes the profit is expressed as a percentage of SP. This percentage figure is called the Margin. Margin = Profit/SP * 100
1. Find the margin percentage if the profit percentage is 6.66 %.
6.66 % i.e. 1 is of the CP, so it is best to assume the CP = 15. Hence profit = 1 and SP = 16. And now the margin percentage is 1/16 = 6.25%.
1) If the cost price is 25 % less than the selling price, find the profit percentage.
2) An article sold at a certain price results in a loss of 7 % whereas when it is sold at Rs. 100 more, it results in a 13 % profit. Find the cost price of the article.
3) An article sold at Rs. 423 resulted in a loss of 10 %. What should be the selling price to result in a profit of 10 %?
4) A man gains 10 % when he sells the article at a certain price. Find his profit percentage if he increases the selling price by 50 %.
5) The profit earned by selling an article at 1060 is 20 % more than the loss incurred by selling the article for Rs. 950. Find the cost price of the article.
Practice more problems on Profit and Loss here