 Hi and welcome to the session. Today we will learn about prices related to an item or buying and selling. Suppose a shopkeeper buys an item at a certain price and then sends it at some other price. Then the buying price of an item is known as its cost price and is denoted as CP in short form. And the price at which that item is sold is known as its selling price and is denoted as SP in short form. Now if cost price that is CP is less than the selling price that is SP of an item then the shopkeeper makes a profit and the profit is equal to selling price minus cost price. If cost price is equal to selling price then there is no profit and no loss and if cost price is greater than selling price then the shopkeeper bears a loss and the loss is equal to cost price minus selling price. Now let's see how to find profit or loss as a percentage. Profit and loss can always be converted into percentage and is always calculated on cost price. So profit percent is given by profit upon cost price into 100 and loss percent is given by loss upon cost price into 100. Now out of three quantities that is cost price, selling price and profit or loss or profit percent or loss percent if two quantities are given then we can always find out the third quantity. Let's take an example. Suppose we are given that selling price of an article is rupees 250 profit percent is 25 percent and we need to find the cost price of the article. So for this first of all we know that profit is equal to 25 percent of cost price. So this will be equal to 25 percent means 25 upon 100 of cost price means into cost price. Now we know that selling price is equal to cost price plus profit. So this will be equal to cost price plus 25 upon 100 into cost price. Now we are given that selling price is equal to rupees 250 so here we will have 250. So this implies 250 is equal to cost price into 1 plus 25 upon 100 which will be equal to cost price into 125 upon 100. On simplifying this we get cost price is equal to 250 into 100 upon 125 which is equal to 200. Thus cost price of the article is equal to rupees 200. Now our next topic is charge given on borrowed money or simple interest. Money borrowed by a person is known as some borrowed or principal and principal can be denoted by the capital letter P. Now the borrower uses the money borrowed for some time before returning it. So for keeping that money for some time the borrower needs to pay some extra money. So the extra money paid by the borrower is known as interest and is denoted by the capital letter I. Now the amount that the borrower needs to pay after an year is the sum borrowed that is principal plus interest and the amount is denoted by the capital letter A. So we have amount A is equal to principal plus interest. Now interest is generally given in percent for a period of 1 year and is written as say 10% per year or per annum. And in short form it is written as 10% per annum and this rate of interest is denoted as r%. Now to find out the interest paid for 1 year we use the formula P into r upon 100. Let's take an example. Suppose we are given that the principal P is equal to rupees 4000. Rate that is r% is equal to 20% per annum and we need to find interest paid at the end of 1 year. Now we know that interest is equal to P into r upon 100. So here interest to be paid will be equal to rupees 4000 into 20 upon 100 which will be equal to rupees 800. Now let's see how to find out the interest paid for multiple years. If the money is borrowed for more than 1 year then interest is calculated for the period the money is kept for. Now in the above example if the money is kept for more than 1 year say 2 years then the interest will be paid as rupees 800 for the first year and again rupees 800 for the second year. So that means rupees 1600 will be paid at the end of 2 years as interest. Now this way of calculating interest where principal does not changes is known as simple interest. Now let's see how to calculate the simple interest for the principal rupees P at a rate of r% per annum for t years. Now here t years is the time for which the money is borrowed. So here simple interest or i will be given by principal into rate into time upon 100 that is P into r into t upon 100. And the amount that is to be paid after t years will be equal to principal plus simple interest. We will take an example for this. Suppose we are given principal P is equal to rupees 6050 rate that is r% is given to be 6.5% per annum and the time is given to be 3 years. And we need to find the interest to be paid at the end of 3 years and amount to be paid. So first of all we will find simple interest that is i which is equal to P into r into t upon 100. So this will be equal to rupees 6050 into 6.5 into 3 upon 100 which will be equal to rupees 1179.75. Now let's find the amount to be paid at the end of 3 years. We know that amount is equal to principal plus simple interest. So here amount will be equal to rupees 6050 plus rupees 1179.75 and this will be equal to rupees 7229.75. With this we finish this session. Hope you must have understood all the concepts. Goodbye, take care and have a nice day.