Download presentation

Presentation is loading. Please wait.

Published byJaren Osswald Modified over 2 years ago

1
**Quantitative Methods Chapter 3 – RATIO & PROPORTION Session 3**

Quantitative Methods Chapter 3 – RATIO & PROPORTION Session Pranjoy Arup Das

2
Ratio is the quantitative relationship between two or more quantities of the same kind which combine to form a single unit. Vice Versa, when a single unit / amount is divided into two or more parts of the same kind, the quantitative relationship between the quantities of the parts is expressed in the form of a ratio. Eg. Suppose 10 boys and 6 girls get together to form a club, the total no. of members of the club will be 16 and the ratio of male members : female members is… Ratio of males to females = 5:3 This means that in every 8 member group, there are 5 males and 3 females. The first term of a ratio, which is 5 in our case, is called the antecedent and the second term, which is 3 in our case, is called the consequent. And 8 is called Sum of the ratio terms. A RATIO IS ALWAYS EXPRESSED AS A VULGAR FRACTION NOT IN DECIMALS

3
Eg 2. The total no. of members of a club is 20 and the ratio of male members : female members = 3 : 2. We have to find the no. of male and female members. Solution 1, Since Males : Females = 3 : 2 No. of Males / No. of females= 3/2 No. of Males = (3/2) * No. of females Since total members is 20 Males + Females = 20 => (3/2)* Females + Females = 20 Females = 8, Males = 3/2 * 8 = 12 Solution 2 – Let the no. of male members be 3x and no. of female members be 2x, where x is a non-zero number. 3x + 2x = 20 => x = 20/5 = 4 So the no. of male members = 3 * 4 = 12 the no. of female members = 2 * 4 = 8.

4
Solution 3 – Since the ratio of boys to girls is 3:2, this means that out of 5 members, 3 are boys & 2 are girls. Then out of 20 there are (3/5) * 20 = 12 boys And out of 20, there are (2/5) * 20 = 8 girls Point to note: If P comprises of A & B which exist in the ratio a:b, then Quantity or Value of A = a / (a + b) * P Quantity or Value of B = b / (a + b) * P (a+b) is called the sum of the ratio terms. So in the above case, P = 20, a = 3, b = 2 No. of boys = {3/(3+2)} * 20 = (3/5) * 20 = 12 No. of girls = {2/(3+2)} * 20 = (2/5) * 20 = 8

5
**Eg 3. The ratio of male members to female members of a club is 4 : 5**

Eg 3. The ratio of male members to female members of a club is 4 : 5. There are 40 females. We need to find the no. of male members. Solution 1 – Let the no. of male members be 4x and no. of female members be 5x, where x is a non-zero number. 5x = 40 => x = 8 So the no. of male members = 4 * 8 = 32. Solution 2 – Point to note: If A & B are the ratio a:b, it means that Quantity or Value of A / Quantity of B = a/b Quantity or Value of A = (a /b) * Quantity of B And Quantity or Value of B = (b/ a) * Quantity of A So in the above case, a = 4, b = 5, B = 40 No. of male members = 4/5 * 40 = 32

6
Proportion TWO MEANINGS: 1) Proportion is the ratio of a part of something to the whole of that something. If A is a part of B, the ratio A : B will provide us the proportion of A (which is a part of B) to B (the whole). Just as Percentage – out of 100, Proportion – out of 1. Eg. In a class of 42 students, 24 students own a Samsung phone, 14 own a Nokia phone and 3 own a Micromax phone and 1 person owns a Karbonn phone. What is the proportion of students owning a samsung phone? What proportion and percentage of students own a Micromax phone? Proportion = = 24 / 42 = 4/7 = 0.55 Proportion is always between 0 and 1. It helps in Probability theory.

7
**2nd Meaning : Proportion also refers to the equality of two ratios.**

If a:b = c:d, then a, b, c & d are in proportion. Here b & c are called the means and a & d are called the extremes. Product of means = product of extremes, i.e., b*c = a*d If a:b=c:d, then d is the fourth proportional to a, b, & c. If a:b = b:c, then c is the third proportional to a & b.

8
**Three approaches to a ratio related problem :**

If ratio of A to B = p : q, and the sum of A & B is M then to find the values of A & B, you may follow any of the 3 approaches to solve : APPROACH 1: Since A:B = p:q, this means So, A = (p/q) * B B = (q/p) * A APPROACH 2 : Value of A can be assumed as px and value of B can be assumed as qx. So the sum of A & B = px + qx. Therefore, px + qx = M APPROACH 3: Value of A = {p/(p+q)} * M Value of B = {q/ (p+q)} * M

9
**Since , Meena’s age : Meera’s age = 4 : 3 **

RSA EX 12A, Pr no. 36 Page 254: The ratio of Meena’s age and Meera’s age is 4 : 3 and the sum of their ages is 28 years. What will be the ratio of their ages after 8 years? APPROACH 1: Since , Meena’s age : Meera’s age = 4 : 3 Meena’s age / Meera’s age = 4 / 3 => Meenas age = (4/3) * Meera’s age And it is given that Meena’s age + Meera’s age = 28 years (4/3) * Meera’s age + Meera’s age = 28 => Meera’s age = 28 * 3 / 7 = 12 years Meena’s age = (4/3) * 12 = 16 years Ratio of their ages after 8 years = ______ =______

10
APPROACH 2: Let Meena’s age be 4x years and Meera’s age be 3x years 4x + 3x = 28 => x = 4 So, Meena’s age = 4*4 =16 years Meera’s age = 3*4 = 12 years Ratio of their ages after 8 years = ______ :______

11
APPROACH 3: Since meena :meera = 4:3, and Sum of their ages is 28 years Meena’s age = 4/(4+3)*28 = 4/7 * 28 = 16 years Meera’s age = 3/(4+3)*28 =3/7 * 28 = 12 years So the ratio of their ages after 8 years = _____:_____

12
**Divide Rs. 420 among A,B,&C in the ratio 1/3 : 5/6 : 7/9**

Ex. 7 Page 250 : Divide Rs. 420 among A,B,&C in the ratio 1/3 : 5/6 : 7/9 Point to note: If a sum of money Rs. S is to be divided amongst A, B & C in the ratio a:b:c, then A’s Share = a / (a+b+c) * S B’s Share = b / (a+b+c) * S C’s Share = c / (a+b+c) * S (NOTE : a+b+c is referred to as sum of the ratio terms) Since Rs. 420 is to be divided amongst A,B & C in the ratio 1/3 : 5/6 : 7/9 Sum of the ratio terms = (1/3) + (5/6) + (7/9) = 35/18 A’s share = = = Rs.__________

13
**Let the total sum of money be Rs. M **

Exer. 12A, Pr no. 40 Page 254: A sum of money is divided among W,X,Y & Z in the ratio 3:7:9:13 respectively. If the shares of W & Y together are Rs , then what is the difference between the X’s share and Z’s share? Solution : Let the total sum of money be Rs. M Rs. M is to be divided in the ratio W:X:Y:Z = 3:7:9:13 So W’s share = 3/( ) * M = Rs. (3/32) * M & Y’s share = Rs. (9/ 32) * M Given that W ‘s share + Y’s share = Rs (3/32)*M + (9/32)*M = 11172 M = So now, X’s share = (7/32) * ________ = Rs. ________ Z ‘s share = (13/32) * ________ = Rs. ________ Difference between X & Z ‘s share = Rs. ____________ Rs

14
**Solution : Ratio of milk to water = 5 :3 & Milk + Water = 20 Lts **

Pr no. 47 Page 255: In a 20 litre mixture of milk and water, the ratio of milk and water is 5 : 3. If 4 litres of the mixture is taken out and 4 litres of milk is added, what will be the ratio of milk and water in the new mixture? Solution : Ratio of milk to water = 5 :3 & Milk + Water = 20 Lts Quantity of milk in 20 Ltrs of the mix = 5/8 * 20 = 12.5 Lts Quantity of water in 20 Ltrs of the mix= 3/8 * 20 = 7.5 Lts Given that 4 Ltrs of the mixture of milk and water is removed: Quantity of Milk in 4 L of the mixture = 5 /8 * 4 = 2.5 Lts So the total qnty of milk becomes = 12.5L – 2.5 L = 10 Lts Qnty of water in 4 L of the mixture = 3/ 8 * 4 = 1.5 Lts So the new qnty of water = 7.5 L – 1.5 L = 6 Lts Now, if 4 ltrs of milk is added to the new mixture, Quantity of milk becomes _______ Lts = And qnty of water___________________________ So the new ratio of milk : water = _______ = ________ 10 Lts 14 Lts remains the same = 6 Lts

15
**Solution : If A: B: C = 3:5:7, the A : B = 3:5 and B : C = 5 : 7 **

Pr no. 82 Page 257: The salaries of A,B & C are in the ratio 3:5:7. If these salaries are increased by 50%, 60% and 50% respectively, then what will be the ratio of the new salaries? Solution : If A: B: C = 3:5:7, the A : B = 3:5 and B : C = 5 : 7 So A / B = 3 /5 That means, So the ratio of A’s & B’s new salary = 9/2 : 8 And since B/C = 5/7 So the ratio of B’s & C’s new salary = 8 : 21/2 So the new ratio of A : B : C = =_________________

16
Practice session Arithmetic, RS Aggarwal, Exercise 12A, Problem nos. 2, 9, 35, 37, 44, 48, 50, 53, 82, 85, 87, 95, &113. RECAP: Three approaches to a ratio related problem : If ratio of A to B = p : q, and the sum of A & B is M then to find the values of A & B, you may follow any of the 3 approaches to solve : APPROACH 1: Since A:B = p:q, this means So, A = (p/q) * B B = (q/p) * A APPROACH 2 : Value of A can be assumed as ‘px’ and value of B can be assumed as ‘qx’. So the sum of A & B = px + qx. Therefore, px + qx = M APPROACH 3: Value of A = {p/(p+q)} * M Value of B = {q/ (p+q)} * M

Similar presentations

OK

Copyright © 2012, Elsevier Inc. All rights Reserved. 1 Chapter 7 Modeling Structure with Blocks.

Copyright © 2012, Elsevier Inc. All rights Reserved. 1 Chapter 7 Modeling Structure with Blocks.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on cash flow management Ppt on network layer Ppt on life in 2050 Ppt on natural resources and conservation in south Ppt on abs system in bikes Free download ppt on obesity Ppt on area of parallelogram and triangles in real life Ppt on resources utilization and development Ppt on information communication technology Ppt on natural resources for class 10