Ratio and Proportion, Indices and Logarithm

Paper 4: Quantitative Aptitude- Mathematics Chapter 1 Part II: Proportion Ms. Ritu Gupta, MA (Maths.)

Learning Objectives

What is proportion

Properties of Proportion

and its application

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Proportion • An equality of 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.

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Properties - Cross-multiplication

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Properties - Invertendo

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Properties - Alternendo

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Properties - Compounendo

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Properties - Dividendo

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Properties - Compondeo and Dividendo

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Properties - Sum of antecedents to the Sum of consequents

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Properties - Sum of 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

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Illustration - 13

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Illustration - 14

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Illustration - 15

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Illustration - 16

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Illustration – 16 – Continued

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Illustration – 16 – Continued

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Illustration - 17

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Illustration - 18

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Illustration – 18 - Continued

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Illustration - 19

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Illustration - 20

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Illustration 21 The price of 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.

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Illustration 21 - Continued

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Illustration - 22

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Illustration – 22 - Continued

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Illustration 23 A sum of 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

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Illustration 23 - Continued

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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.

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econsequenc of Productsantecedent of Product=RatioCompounded

Illustration 24 – Continued

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Illustration - 25

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Illustration – 25 - Continued

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Illustration – 26 A man 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

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Illustration – 26 – Continued

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Illustration – 26 – Continued

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Illustration 27

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Illustration 28

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Illustration – 29 The sum 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

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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)

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Illustration – 30

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Illustration – 30 – Continued

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Thank You

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