 Hello and welcome to the session. In this session first we will discuss ratios and percentages. We know that ratio means comparing two quantities. Consider a basket in which we have four red balls and six black balls. Let's try and compare the red balls and the black balls in the basket. Using the ratios. So ratio of the number of red balls to the number of black balls is 4 is to 6. Now this comparison can be done by using fractions also. That is we can write 4 upon 6 that is equal to 2 upon 3. And thus we can say that the number of red balls to third the number of black balls. We can also do this comparison using percentages. Now in all we have 10 balls in the basket. So out of the 10 balls the number of red balls is 4. We know that person means 100. So we will find out the number of red balls out of 100. So out of 100 balls the number of red balls is given by 4 upon 10 into 100 and this is equal to 40. That is out of 100 balls 40 are red balls. So we say the basket has 40 percent red balls. And the black balls in the basket are equal to 60 percent. Since we have 100 minus 40 is equal to 60. So this is how we can compare two quantities using ratios and percentages. Next we discuss increase or decrease percent. Suppose we have that price of a dress is given as rupees 1000 and the shopkeeper announces 10 percent off on the dress. Now the percentage decrease in the price implies finding the actual decrease followed by its subtraction from the original price. First let's find out the reduction. Reduction is equal to 10 percent off the price of the dress that is rupees 1000. This is equal to rupees 10 upon 100 into 1000. That is reduction is equal to rupees 100. Now the new price of the dress is equal to the old price of the dress that is rupees 1000 minus the reduction which is rupees 100 and this is equal to rupees 900 would be the new price of the dress. Next we have discount. Discount is a reduction given on the marked price that is NP of the article. We have discount is equal to the marked price minus the sale price. We can also calculate the discount when discount percentage is given to us. Then we have discount is equal to discount percent of the marked price. Consider that the marked price NP of an article is given as rupees 500 and the discount given on this article be 10 percent. First let's find out the amount of discount given on the article. Now the discount is equal to discount percent that is 10 percent off the marked price that is rupees 500. Now this is equal to rupees 10 upon 100 into 500 which is equal to rupees 50. Thus the discount given on the article is rupees 50. We know that discount is equal to marked price minus the sale price. So we have sale price is equal to the marked price that is rupees 500 minus the discount that is rupees 50 and this is equal to rupees 450. This is the sale price of the article. Next we have estimation percentages. Suppose that when we go for shopping the bill amount that we get is rupees 375.60 and the shopkeeper gives us a discount of 15 percent on the total bill. Now let's estimate the amount that we need to pay at the shop. For that first we need to round off this bill amount to nearest tens. So we get the bill amount is equal to rupees 380. Then we take 10 percent of this that is rupees 10 upon 100 into 380 is equal to rupees 38. Then we take half of this 38 and this is equal to rupees 19. Then we add these two amounts that is rupees 38 plus rupees 19 is equal to rupees 57. Thus we say the bill amount will be reduced by rupees 57 or by about rupees 55. Thus we have the amount to be paid would be equal to rupees 380 minus rupees 55 and this would be equal to rupees 325 approximately. So this is the amount that we need to pay after we get a discount of 15 percent on the total bill amount. Next we discuss prices related to buying and selling profit and loss. First let's see what are the overhead expenses. Additional expenses made after buying an article are included in the cost price and are known as overhead expenses. Then the cost price that is CP is equal to the buying price the overhead expenses. Now if we have that the selling price that is SP is more than the cost price CP then profit would be made and this would be equal to SP minus CP. And if the cost price that is CP is more than the selling price that is SP then there would be loss and this would be equal to CP minus SP. Then we also have profit percent is equal to profit upon the cost price CP into 100 and then loss percent is equal to loss upon CP into 100. Consider that the buying price of a cycle is rupees 700 and then the overhead charges are rupees 50 and the profit is 5 percent. Let's find out the selling price SP of this cycle. First we need to find the cost price CP and this is equal to the buying price that is rupees 700 plus the overhead charges that is rupees 50. So this comes out to be equal to rupees 750. Now we know that profit percent is equal to profit upon CP into 100. So we have that profit is equal to profit percent that is 5 into the CP that is 750 upon 100 and this comes out to be equal to rupees 37.50. So this is the profit. Now since we know that profit is equal to SP minus CP so from here we have SP is equal to profit that is rupees 37.50 plus CP which is rupees 750. Now this would be equal to rupees 787.50. So this is the selling price of the cycle. Next we have sales tax value added tax. Sales tax that is ST is the amount which we pay when we buy items. It is charged by the government or the sale of an item. So these days the prices include the tax which is known as value added tax that is VAT. Then we have sales tax is equal to tax percent of the bill amount. Consider the cost price CP of a soap is rupees 50. Then sales tax added on the purchase of the soap is 5%. Let's try and find out the buying price of the soap. We have sales tax is equal to tax percent that is 5% of the bill amount that is rupees 50. This would be equal to rupees 5 upon 100 into 50 and this is equal to rupees 2.50 that is this much sales tax would be added on the purchase of the soap of rupees 50. Thus we have the buying price would be equal to the cost price of the soap rupees 50 plus the sales tax that is rupees 2.50 and this is equal to rupees 52.50 is the buying price of the soap. This completes the session. Hope you have understood the concept of ratios and percentages, increase or decrease percent, then discount, estimation and percentages, profit and loss and sales tax on VAT.