 Hello and welcome to the session. In this session first we shall discuss percent change mark ups and downs on commodities. In this session we shall learn the effect of percent change that is percent increase or percent decrease. If I say last year 2000 people came to the city museum and this year 3000 people came to visit city museum we can see that there is an increase in number of people visiting the museum. Then can we find by what percent there is an increase in number of people visiting the museum this year than last year. This is called percent change and this change can be increasing or decreasing. So we can say percent change is the ratio that compares change in quantity to the original amount. So we write percent change is equal to amount of change upon original amount when original amount increases then percent change is called percent increase so we can write percent increase as new amount minus original amount upon original amount also when original amount decreases then percent change is called percent decrease so we can write percent decrease original amount minus new amount whole divided by original amount. So we can say if amount of change is positive then there is increase in percent and if the amount of change is negative then there is decrease in percent. For example if we need to find out percent change from 10 miles to 13 miles Now here we see that the original amount increases so the percent change is increasing so we first find the amount of change which is equal to new amount minus original amount which is equal to 13 minus 10 that is 3 as we know percent increase is given by the formula new amount minus original amount whole divided by original amount and here we have the amount of change that is new amount minus original amount as 3 upon original amount which is equal to 10 so we have 3 by 10 which can be written as 0.3 and which can be written in the percentage form as 3 by 10 into 100 percent which is equal to 40 percent so we can say that there is 50 percent increase now we are going to discuss mark ups and downs suppose a shopkeeper got an item for 100 dollars now to make profit he increases the price and sells the item at 105 dollars so we can say that selling price is now 105 dollars increase is of 5 dollars and this increase is called markup we increase from what we store based to the selling price is called markup so we can say markup is equal to markup percentage of original price and selling price is equal to original price plus markup suppose a store pays 90 dollars for the skateboard and the markup is given as 20 percent then what will be the selling price as we know from above that markup is markup percentage of original price so here markup will be equal to 20 percent of 90 which is equal to 20 by 100 into 90 that is 2 into 9 which is equal to 18 so the selling price will be equal to original price plus markup which is equal to the original price is given as 90 dollars plus the markup is equal to 18 dollars so we get 108 dollars the selling price of the skateboard is equal to the sum of the original price and the markup now we are going to discuss markdown it is the discount given on an item and discount is a decrease in the original price of the item and we can write markdown or discount is equal to markdown percentage of original price and selling price will be equal to original price minus markdown now we shall study 2 methods of finding selling price when discount percent is given let us take an example an item originally priced at 55 dollars is marked 25 percent of what is the sale price here a discount of 25 percent is given so first we will find markdown and markdown 25 percent of the original price of 55 dollars so this is equal to 25 by 100 into 55 dollars which is equal to 55 upon 4 that is 13.75 dollars so we got the markdown price as 13.75 dollars and we know that sale price is equal to original price minus markdown here the original price is given as 55 dollars minus markdown price which is equal to 13.75 dollars so here we get the value of sale price as 55 minus 13.75 dollars that is 41.25 dollars thus the sale price is 41.25 dollars now we shall solve the same question using another method in the above question we are given the discount as 25 percent now we will find percentage of original price that is today we have 100 percent and discount is given by 25 percent so remaining is given by 100 percent minus 25 percent which is equal to 75 percent so we can say 25 percent discount is same as paying 75 percent of original price so sale price would be equal to 75 percent of original price and 75 percent of original price is equal to 75 upon 100 into 55 dollars which is equal to 55 into 3 that is 165 by 4 dollars which can be written as 41.25 dollars so these are the two methods of finding selling price when discount percentage is given now we shall study percent error and percent error is given by the formula that is approximate value minus exact value whole divided by exact value into 100 percent if we say a person thought 70 people would turn up to the concert but in fact 80 did here if we have to find the percent error we have the approximate value that is 70 minus exact value that is 80 upon exact value that is 80 into 100 percent which is equal to 70 minus 80 is minus of 10 upon 80 into 100 percent and this is equal to minus of 100 by 8 which is equal to minus of 12.5 percent so we can say that person was an error by minus of 12.5 percent this error is minus of 12.5 percent means there is decrease in what was approximated this means that person had underestimated the value and to avoid negative sign we can take absolute value of percent error this complete session hope you enjoyed this session