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- 1. PERCENTAGE is one of the most commonly used mathematical concept in real life. This is simple concept with various concept with various applications. Hence, you are expected to be absolutely confirm with this concept. In order to increase your confirm levels, you will do well to keep calculating percentages mentally, whenever you get an opportunity to do so in real life PERCENTAGE
- 2. PERCENTAGE OF A NUMBER Percent means, per 100. here “cent” stand for 100 . To find the percentage of a number, convert the %age into fraction and multiply the resulting fraction with the number, e.g. 60% of 500 = 60 100
- 3. CONVERSION OF A FRACTION OR A DECIMAL INTO A PERCENT A fraction or decimal can be converted in to a percentage by simply multiplying it by 100. so, the fraction 1/5 expressed as a percentage is 1/5*100 = 20% And the decimal 0.05 expressed as a percentage is 0.05 * 100 = 5%
- 4. Converting a percentage into a fraction A %age when divide by 100 is converted into a fraction. So 20% as a fraction is 20/100 = 1/5 The % sign is dropped when we divide the % by 100. Fraction of a number To determine the fraction of a number we multiply the fraction and the number. Therefore,
- 5. Fraction of a fraction and relative percentage To find the fraction of a fraction we multiply both the fractions.
- 6. Type of questions Examples If A’s income is x% of B’s income and B’s income is given. Then find A’s income. A’s income is 40% of B’s income. If B’s income is Rs.10,000, what is A’s income?
- 7. Approach
- 8. Type of questions Examples If A’s income is r% more than of B’s income, than by how much percent is B’s income less than A’s income? X’s income is 25% more than Y’s. By how much % is Y’s income less than X’s income?
- 9. Approach
- 10. Type of questions Examples Approach If A’s income is r% less than of B’s income, than by how much percent is B’s income more than A’s income? X’s income is 20% less than Y’s. By how much % is Y’s income more than X’s income?
- 11. Approach
- 12. Type of questions Examples If A’s income is r% less than of B’s income, than by how much percent is B’s income more than A’s income? X’s income is 20% less than Y’s. By how much % is Y’s income more than X’s income?
- 13. Approach
- 14. Type of questions Examples If the price of a commodity increases by r%, find the % decrease in the consumption given that expenditure remain same If the price of potato is increased by 20%, by how much should the consumption be decreased so as to maintain the same expenditure?
- 15. Approach
- 16. Type of questions Examples If price of one unit changes by a% and the number of units consumed changes by b%, than what is the % change in expenditure If the price of potato is increased by 20% and consumption decreased by 10%, what will be the percentage change in expenditure?
- 17. Approach
- 18. Type of questions Examples 1. If the population of a country increases in the first year and decreases in second year. The population of a town is 18,000. It increases by 10% during first year and by 20% during the second year. The population after 2 years will be
- 19. Approach
- 20. Alternative Method Successive increments of 10% and 20% = 32%. Then, population will increase by 32% of 18000 = 5760 population after 2 years will be 18000+5760 = 23760
- 21. EXAMPLES:- A’s income is 70% of B’s income. B’s income is 50% of C’s income. If C’s income is Rs. 1, 00,000. What is A’s income? If the price of an item is increased by 20% and then a discount of 10% is given on the increased price, what will be the effect on sale? The number of seats in an auditorium is increased by 25%. The price on a ticket is also increased by 12%. What is the effect on
- 22. The length of a rectangle is increased by 10%. What will be the percentage decrease in its breadth so as to have the same area? In a market survey, 20% opted for product B. The remaining individuals were uncertain. If the difference between those who opted for product B and those who were uncertain was 720, then how many individuals were covered in the survey? Of the total amount received by Kiran, 20% was spent on purchases and 5% of the remaining on transportation. If he is left with Rs. 1520, the initial amount was 5% of income A is equal to 15% of income B and 10% of income B is equal to 20% of income C. if income of C is Rs. 2,000 , then the total income of A, B and C is
- 23. Arvind spend 75% of his income. His income is increase by 20% and he increases his expenditure by 10%. His saving is increased by how many percent? Two numbers are respectively 19% and 70% more than a third number. What percentage is the first number out of the second? Salary of A, B and C are in the ratio of 1:2:3. Salary of B and C together is Rs. 6,000. By what percent is the salary of C more than that of A? The price of rice increased from Rs. 15 by 15% and then reduce by 30 paise. What was the net increase? Successive discount of 30%, 20% and 10% are equivalent to a single discount of?
- 24. SUPPOSE that you are selling some article. You can sell that article at the price you bought, more than that or less than that, means in any such transaction three cases will be arise PROFIT, LOSS AND DISCOUNT
- 25. THEORY AND CONCEPT In day to day life we sell and purchase the things as per our requirement. A customer can get things in the following manners: Manufacturer (or producer) Whole seller (dealer) (shopkeeper) Retailer (or sells person) Customer
- 26. TERMINOLOGY COST PRICE – The money paid by the shopkeeper to the manufacturer or whole seller to buy the goods is called the cost price(CP) of the goods purchased by the shopkeeper. Selling Price (SP) – The price at which the shopkeeper sells the goods is called the selling price (SP) of the goods sold by the shopkeeper. NOTE- If an article is purchased for some amount and three are some additional expenses or transportation labor, commission etc., these are to be added in the cost price. Such expenses are called overhead expenses or overheads.
- 27. a. Cost price (C.P.) > selling price (S.P.) b. Cost price (C.P.) < selling price (S.P.) c. Cost price (C.P.) = selling price (S.P.) as a result either you will have profit (p) or loss (L) or no profit or no loss
- 28. Profit & Loss can be defined in two ways A. In term of absolute amount: suppose that if CP of an article is Rs.200 and SP is 300. so profit is SP-CP = 300-200 = 100. B. In terms of percentage: wherenever you want to calculate the prpofit & loss in terms of percentage, it is always calculated on the basic of CP. In the above example the profit is Rs. 100on CP of 200, so the profit % is 50%
- 29. IMPORTANT FORMULAE Profit = SP-CP Loss = CP – SP Profit percentage =
- 30. NOTE – Profit & loss is always calculated on the basic of cost price unless otherwise mentioned in the problems
- 31. MARK UP AND DISCOUNT MARKED PRICE – Basically to avoid the loss due to bargaining by the customer and to get the profit over the cost price trader increases the cost price by a certain value, this increase in the value over cost price is known as markup and the increase price is called the marked price or printed price or list price in the goods. Marked price = CP+ Markup Marked Price = CP +(% markup on CP)
- 32. Discount : discount means reduction of marked price to selln at a lower rate or literally discount means concession. Basically it is calculated on the basic of marked price. Selling price = marked price – discount Selling price = Marked price – ( discount % on MP)
- 33. Since markep price = CP+ % markup on CP remember markup is calculated on the basic of CP while discount is calculated on the basis on MP in general, CP>SP<MP at profit CP=SP<MP at no profit no loss SP<CP<MP at loss
- 34. Type of questions Examples 1. If A sells to B at a profit of x%; B sells to C at a profit of y% and C pays Rs. P for it, find the cost for A. A sells a cycle to B at a profit of 10%, B sells to C at a profit of 20%. If C pays Rs. 264 for it, how much did A pay for it?
- 35. Type of questions Examples 1. If cost price of A articles is equal to the selling price of B articles, find the profit percentage. The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percentage.
- 36. Type of questions Examples 1. The cost price of two articles is same. If one is sold at a X% profit and the other at a loss of X %, find the profit or loss percentage. Amit buys 2 cows for Rs. 200 each. He sells one at a profit of 10% and the other at a loss of 10%. Find his profit or loss percentage.
- 37. Approach For the equal profit & loss %age, there is no profit no loss
- 38. Type of questions Examples 1. The selling price of two articles is same. If one is sold at a X% profit and the other at a loss of X %, find the profit or loss percentage. Amit sells 2 cows for Rs. 200 each. On one he gets a profit of 10%, while losing 10% on other. What is his overall profit or loss percentage?
- 39. Approach For the same selling price & equal profit & loss percentage there is always a loss of
- 40. Type of questions Examples 1. If x % discount on an articles is given on cash payment. Find the %age that should be marked above the cost price so as to make a profit of y%. A dealer allows a discount of 7% for cash payment. How much %age above the cost price should he marks his goods to make a profit of 10%
- 41. Approach
- 42. Type of questions Examples 1. If a dealer sells goods at cost price but uses faulty weight, find his gain percentage. A dishonest dealer professes to sells to sell his goods at cost price, but he uses weight of 960 gm for 1 kg. find his profit %age.
- 43. Approach
- 44. EXAMPLES :- A boy buys eggs at 10 for Rs. 1.80 and sells them at 11 for Rs. 2. What is the profit or loss %? a man bought 80 kg of rice for Rs. 88 and sold it at a loss of as much money he received for 20 kg. At what price did he sell it? goods are purchased for Rs. 450 and one-third is sold at a loss of 10%. At what profit %age should the remainder be sold so as to gain 20 % on the whole transaction?
- 45. a reduction of 10% in the price of sugar enables a man to buy 25 kg more for Rs. 225. What is the original price of sugar? a man sells an articles at a profit of 25%. If he had bought it at 20% less and sold it for Rs. 10.50 less, he would have gained 30%. Find the C.P. of the articles. if a commission of 10 % is given on the marked price of an articles, the gain is 25%. Find the gain %age, if the commission is increased to 20%. peanuts are sold at 60 per rupee. If the vendor decides to hike the S.P. by 20%, how many peanuts can be bought per rupee?
- 46. Sumeet buys 9 books for Rs. 100 but sells 8 for Rs. 100. What is the next %age of profit? A person earns 15% on an investment but losses 10% on another investments. If the ratio of two investments be 3 : 5, what is the gain or loss on the two investments taken together? Vivek purchased 120 tables at a price of Rs. 110 per table. He sold 30 tables at a profit of Rs. 12 per table and 75 tables at a profit of Rs. 14 per table per table. The remaining tables were sold at a loss of Rs. 7 per table. What is the average profit per table?

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