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Ratio Proportion and Partnership

Aptitude

Session 1: Ratio, Proportion and Partnership

 Lesson Plan: 90 minutes

Objective: 

To help students understand the basics of comparison between two quantities in terms of magnitude. Students get to know that comparison of two quantities is meaningless if they are not of same kind or in the same units. We do not compare 5 boys with 7 computers or 15 kilometres with 4 tables. Therefore, for comparison, it is necessary to explain them in same units. Students would be able to calculate share of profit they get or loss they would bear if they invest in same or different proportion with their partner.

To enable learners solve problems of any kind related to Ratio, Proportion and Partnership. Participants will be able to deduce solutions in their daily life by using their skills and concepts acquired through this lesson plan discussed in Block A. To enable approach and solve any questions or real life problems related to the lesson.

Total Time: 90 Minutes

Materials Required:  Pen, Notebook.

Instructor Note: This unit deals with the concepts and application of ratio, proportion and partnership. It has to be ensured that since the topics are highly relevant to daily observations and usage, it becomes inevitable to impart sound understanding of the same. Trainer is required to deliver this unit under an engaging environment by using practical examples and competitive activities.

  • Display/distribute handout consisting of questions. Foundation section will compromise 4 questions, instruct students that they will be given 8 minutes to discuss among themselves & solve these 4 questions, whichever group solves maximum problems wins maximum points on the points table (as drawn earlier). Award 5 marks for each correct answer given by a group. Move around the class to check procedures used by students to solve problems. Once time is up, provide solutions and explanations for each question.

  • Switch to moderate level. This section comprises 4 questions and cumulative time allotted will be 10 minutes. All other instructions remain the same.

  • Switch to HOTS. This section comprises 3 questions and cumulative time allotted will be 15 minutes. All other instructions remain the same.

Opening Protocol:

  • Greet the participants.

  • Take attendance.

  • Form groups of participants with each group comprising of 4 members. (For entire session)

  • Draw points table on board and ask participants to name their group with some fancy names. 

  • Inform the participants that the group which tops the points table will be rewarded at the end of session.

  • Recap the previous session by asking 1-2 participants to share with the class what they learnt and did in the previous session.

3 Minutes

Opening Activity:

  • Okay students, today we are embarking upon our journey to learn ratio, proportion and partnerships. We would be dealing with these individual yet interrelated concepts in depth. But before beginning let me ask you how many of you have come through the term ratio?

             Ok so, that means you people do have the basic acquaintance with this. 

   

  • So, ratio in its simplest form is the comparison of two quantities by division. It is a relation that one quantity bears to another with respect to magnitude. In other words, ratio means what part of one quantity is of the other. The quantity may be of the same kind or different kinds.

  • Now, someone tell me about the word proportion. So, yes you guys were near to the explanation of this term.

  • Look at the picture above, now try to understand that for building any partnership, what we need is partners and their individual contribution, Here, we see the two batsmen have contributed their individual parts 

            of 33 and 63 respectively to build a partnership of 100.

  • Now, it is to be understood that we do have another partner, since 33+63=96, and we see that the partnership is of 100. So, any guesses who scored the remaining 4 runs?

             Yes, they came from the extras conceded during this partnership.

  • That being said, now we do have some basic insight of our topics and using them, we would understand the different complexities related, and equip us with the understanding sound enough to approach and solve any question related to these topics.

10 Minutes

Section1: Ratio

As we already know, that ratio is the comparison of two Quantities by division or the relation that one quantity bears to another with respect to magnitude.

If a and b are two numbers, then the ratio a to b is a/b or a÷b and is denoted by a:b. The two quantities that are being compared are called terms. 

The first is called antecedent and the second term is called consequent. 

As always, we would be focusing on the underlying concepts, rather than memorizing formulas, following are the types of ratios you would encounter.

i.) Duplicate Ratio: The ratio of squares of two number is called the duplicate ratio of the two numbers.

For example: 2²5² = 425 is called the duplicate ratio of 25 .

# In the same way we can understand about Triplicate ratio in which the cubes of the two numbers is called the triplicate ratio of two numbers.

iv.) Compound Ratio: When we compound two or more ratios with each other through product or multiplication, the result is simply a compound ratio. Thus, the product of two or more ratios; i.e, ab:cd is a ratio compounded of the simple ratios a:c and b:d. Required compounded ratio = (2/3 x 6/11 x 11/2) = 2/1.

These terms are just for informative purpose, so that you do not get confused on not being familiar with the terminology.

Now, Let’s see some examples and test our learning till now.

Ex.1.) The ratio of boys to girls in a class is 2:3. If total students are 120.Find the number of boys in the class.

Ans.) Here, we see that the ratio of boys to girls is 2:3. Therefore we can deduce that for every 2 boy in the class, we have 3 girls. So, if we consider 2 boys and 3 girls as a group, we have 5 students in total in that group.

Revision Notes for Maths Chapter 12 - Ratio and Proportion (Class 6th) |  askIITians

please explain the componendo and dividendo rule i am unable to understand  or use it effectively - Mathematics - TopperLearning.com | onstw4kk

Section 3 – Partnership: 

We have discussed already that partnership requires partners, whether it is cricket or partners in business.

To run a business or any organisation, we need to have partnerships. There are two types of partners.

i.) Working partners: Those partners who invest the money and manage the business or affairs of organisation are called working partners.

ii.) Sleeping partners: Those partners who merely invest money and do not involve in business affairs are called sleeping partners.

In partnerships, we have mainly three types of conditions related to distribution of profit in business.

Condition 1: 

When time period of investment is constant, then profit of partners will be divided into ratio C1 : C2 : C3 : ……Cn,

Where, C1, C2, C3, …..Cn are investment of respective partners.

 

Condition 2 : 

When amount invested is same for different partners but time period is different, then profit will be divided in the ratio of their time invested, that is

t1 : t2 : t3…… : tn .

Condition 3:

When amount of investment and time period both are different for different partners, then profit will be divided into following ratio.

         C1t1 : C2t2 : C3t3 : …………. : Cntn.

In order to have a clear understanding of the above mentioned cases, lets take an example,

Ex.1.) Three partners undergo a partnership. Their investments are Rs.30000, Rs.45000 and Rs.50000 respectively for the time periods of 4 years, 2 years and  1 year respectively. Find the ratio of their profits.

Ans.)  Here we see that the investments and time period of investments, both are different for all the partners, so we would are provide with Condition 3.

Using the same concept, the ratio of their profits would be,

 

                    C1t1 : C2t2 : C3t3

  • 30000 x 4 : 45000 x 2 : 50000 x 1

  • 30 x 4 : 45 x 2 : 50 x 1

  • 12 : 9 : 5 

Ex.2.) A and B started a business with initial investments in the ratio 5:7 . If after one year their profits were in the ratio 1:2 and the period of A’s investment was 7 months, B invested the money for ?

Ans.) Let investments of A and B respectively be 5x and 7x and period of B’s investment be “t” months.

30 Minutes

Section 1: Foundation.

1.) In a mixture of 40 litres, the ratio of milk and water is 4:1. How much water must be added to this mixture so that the ratio of milk and water becomes 2:3

2.) If three numbers are in the ratio 1:2:3 and half the sum is 18, then the ratio of squares of the numbers is?

3.) Find a third proportional to the numbers 4, 42.

4.) Ansh and Aman enter into a partnership investing Rs.50000 and Rs.40000 respectively. They agree to share their profits in the ratio of their capital. Find the share of Aman in a profit of Rs.22500 after one year.

Section 2: Moderate.

1.) The prices of scooter and TV are in the ratio 3:2. If a scooter costs Rs.600 more than the TV, then the price of the TV is?

2.) The ratio between two numbers is 2:3. If each number is increased by 4, the ratio becomes 5:7. The numbers are?

3.) The value of ‘k’ that must be added to 7, 16, 43, 79 so that they are in proportion is?

4.) Amit, Nitin and Ram entered into a partnership. Amit invested Rs.16000 for 9 months, Nitin invested Rs.12000 for 6 months and Ram invested Rs.8000 for 12 months. At the end of a year there was a profit of Rs.26000. Find the share of Nitin in the profit.

Section 3: HOTS- High order thinking skills.

1.) A mixture contains alcohol and water in the ratio of 12:5. O adding 14 litres of water, the ratio of alcohol to water becomes 4:3. The quantity of alcohol in the mixture is?

2.) The incomes of A and B are in the ratio 3:2 and their expenditures are in the ratio 5:3. If each saves Rs.1000, A’s income is?

3.) A starts a business with a capital of Rs.1200. B and C join with some investments after 3 and 6 months, respectively. If at the end of a year, the profit is divided in the ratio 2:3:5 respectively, what is B’s investment in the business?

8 minutes

Answers

1.) 40 litres

2.) 1:4:9

3.) 441

4.) 12500 

10 Minutes

Answers

1.) 1200

2.) 16 & 24

3.) 5

4.) Rs.6000

15 minutes

Answers

1.) 42 litres

2.) Rs.6000

3.) Rs.2400

Explanation

10 minutes

Closing Activity:

  • Thank you everyone! Now, all of you are clear with your concepts of Ratio, Proportion and Partnership. You will be getting materials for practice that you have to solve by yourself at home and bring doubts, if any. You will be provided handouts with concepts discussed which will help you brush up and revive your concepts any time in future.

  • Trainer needs to calculate total points accumulated on the points table and reward the winning group. In case of a tie between two or more groups, reward each of the winning groups.

  • So, after what we have learnt today, we will be aware of the ratio and proportion in which we are investing and also be aware of the return. We would ensure to utilise the concepts practically to make maximum profit.

1 Minute

Closing Protocol: 

  • Thank the participants for their time.

  • Announce the next time you will be visiting them.

  • Share the topic of the next session.

  • Share the names of reward winning students with nodal officers and institution heads after the session.

Post-session