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Ratio and Proportion, Indices and Logarithm Part 2
The document discusses the concept of proportion in mathematics, defining it as an equality of two ratios and outlining its properties and applications. It includes examples and exercises that illustrate how to calculate proportions, such as determining the cost of items based on given ratios and solving problems involving shares among individuals. Additionally, the document contains illustrations to support the concepts presented and to enhance understanding of the topic.
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Ratio and Proportion, Indices and Logarithm Part 2
- 1. Ratio and Proportion, Indicesand Logarithm Paper 4: Quantitative Aptitude- Mathematics Chapter 1 Part II: Proportion Ms. Ritu Gupta, MA (Maths.)
- 2. Learning Objectives What is proportion Propertiesof Proportion and its application 2
- 3. Proportion • An equalityof two ratio is called a proportion / Four quantities a, b, c, d are said to in the proportion if a : b = c : d (also written as a : b :: c : d) i.e. a/b = c/d i.e. if ad = bc. • The term a and d are called extremes, the term b and c are called the means. The fourth term d is called the fourth proportional of a, b and c taken in order. • If a:b :: b:c, then a, b, c are called in continued proportion, b is called the mean proportional between a and c and c is called the third proportional of a and b. 3
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- 9. Properties - Compondeoand Dividendo 9
- 10. Properties - Sumof antecedents to the Sum of consequents 10
- 11. Properties - Sumof antecedents to the Sum of consequents - Continued Hence, each (a + c + e + ….) : (b + d + f …….) is equal to each ratio or In words - If any number of ratios be equals to one another, then each of these ratio is equal to ratio of the sum of antecedents to the sum of consequents 11
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- 16. Illustration – 16– Continued 16
- 17. Illustration – 16– Continued 17
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- 20. Illustration – 18- Continued 20
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- 23. Illustration 21 The priceof a scooter and a moped are in the ratio 9 : 5. If a scooter costs Rs. 6800 more than a moped, the price of scooter is? (a) Rs. 17,000 (b) Rs. 13600 (c) Rs. 15300 (d) None of these Solution Scooter : Moped = 9 : 5 Let cost of scooter is 9x and cost of moped is 5x. 23
- 24. Illustration 21 -Continued 24
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- 26. Illustration – 22- Continued 26
- 27. Illustration 23 A sumof Rs. 9300 is divided among A,B and C in such a way that share of A and B are in the ratio of 1 : 3 and those of B and C are in the ratio 4 : 5. The amount received by C is (a) 1200 (b) 3600 (c) 4500 (d) 5000 Solution A : B = 1 : 3, B : C = 4 : 5 Multiplying terms of first ratio by 4 and second ratio by 3 we get A : B = 4 : 12, B : C = 12 : 15 27
- 28. Illustration 23 -Continued 28
- 29. Illustration 24 If p: q = 1 : 3 and a : b = 4 : 3, then the value of 4pa + 3qb : 9pa + 4qb is (a) 41 : 82 (b) 27 : 82 (c) 43 : 72 (d) None of these Solution p : q = 1 : 3 and a : b = 4 : 3 Taking the Compounded ratio of LHS and RHS i.e. 29 econsequencofProduct santecedentofProduct =RatioCompounded
- 30. Illustration 24 –Continued 30
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- 32. Illustration – 25- Continued 32
- 33. Illustration – 26 Aman divides his property in such manner that his son’s share to his wife’s share and wife’s share to his daughter’s share are both in the ratio 3 : 1. If the daughter gets Rs. 10,000 less than the son, then the total worth of his property is (a) Rs. 16,250 (b) Rs. 18,250 (c) Rs. 15,250 (d) Rs. 21,250 Solution Let a = Son’s share ; b= Wife’s Share; c=Daughter’s share 33
- 34. Illustration – 26– Continued 34
- 35. Illustration – 26– Continued 35
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- 38. Illustration – 29 Thesum of the ages of 3 persons is 150 years. 10 years ago their ages were in the ratio 7 : 8 : 9. Their present ages are (a) (45,50,55) (b) (40,60,50) (c) (35,45,70) (d) None of these Solution Let the ages of the three persons 10 years ago be 7x, 8x and 9x. Their present ages will be 7x+10, 8x+10 and 9x+10 38
- 39. Illustration – 29– Continued The sum of their present ages is 7x + 10 + 8x + 10 + 9x + 10 = 150 24x =150 – 30 24 x = 120 x = 5 Therefore present ages are 7X5+10, 8X5+10, 9X5+10 (45, 50, 55) 39
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- 41. Illustration – 30– Continued 41
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