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# Profit & Loss

Aptitude(Numeracy & Reasoning)- 21st century literacies

Profit and Loss Lesson Plan

Objective:

• To equip the students with the concepts of profit, loss and related terms.

• To enable learners to solve questions of any kind related to Profit and loss. Students will be able to deduce solutions and develop an ability to understand the concept of profit and loss and its practical applications in daily life.

Total Time: 90 minutes

Instructor Note: This unit would help the learners understand the basics of profit and loss and their applications in daily life. Students learn to use the concepts of percentage for calculating profit and loss, rather than applying formulas. They get an idea of transactions, buying, selling, marked price, discount and their impact on profit and loss.

(After concept discussion & practice) 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 (refer opening protocol). 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 two groups of participants for setting up a competitive approach to learning.(For entire session)

• Draw points table on board and ask participants to name their group with some fancy names like “Aptitude thunders”, “Knights of Mathematics”, “Fantastic Statisticians” etc.

• 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:

• Guys and girls, today we will be learning about the most important element of today’s world, any guesses…. Okay I’ll help you out…so its profit and loss. In fact, the entire economy and concepts of capitalism are based on the so-called ‘profit and loss’ .So, it becomes inevitable to have a sound knowledge of this topic.

• Since then, business transactions have now-a-days become a common feature of life. When a person deals in purchase and sale of any item, he either gains or loses some amount generally. The aim of the entire business is to earn profit after all.

• That being said, now it becomes an imperative call that one should be equipped with concepts rather than formulas for the calculation of profit and loss involved in any transaction.

• And by concepts, I mean the basic understanding which requires the holistic approach to decode the various terms involved and also their applications.

• So, without further ado, let’s get started.

Trainer’s role:

• To make the session interactive as much as possible, as the topic being discussed is relevant in every one’s life and the students come across these terms on a daily basis.

• This could be used as an asset for quick learning when aided by their involvement.

• Explain the calculation and definition.

10

Minutes

Section 1: Understanding the concept of Profit & Loss.

• This unit would comprise of four main terms at large namely:

1.) Cost Price (CP)

2.) Selling Price (SP)

3.) Profit

4.) Loss

5.) Marked Price (MP)

6.) Discount

• Before sailing on this ship of learning these concepts, I need two teams to be formed, who would write all the formulas related to these topics, since I would not be giving you guys the formulas, but the concepts.

And using these concepts we would write all the formulas. Interesting?

So, Let’s unravel them one by one.

• These topics though being distinct are interrelated and dependent on each other.

1.) Cost Price or CP in layman’s terms is the price at which an article has been purchased.

2.) Selling price or SP is the price at which the item has been sold.

3.) Profit is the amount one has gained in carrying out a transaction, i.e. by selling an item.

4.) Loss in the same way is the amount one loses in selling an item.

5.) Marked price or MP is the price that a shopkeeper or your shopping sites label for the item.

6.) Discount is the term which we all want for everything we buy. Ok, Jokes apart, it is the amount that is provided we need not to pay for the MP.

Simple, isn’t it. Trust me, indeed it is that simple as it seems in these definitions, all that is required is a generic and streamlined approach of problem solving, rather than some heavy weight formulas.

• Now, to explain the first four items above and to form a clearer picture I would like to tell you a story. Look at the picture below. • CASE 1: There was a trade fair, in which livestock was being sold. A farmer bought a cow from one trader at Rs.10000. In this transaction the trader earned a profit of Rs.2000.

So from this transaction we could easily infer that the  trader earned a profit on selling the cow to the farmer, so the cost price for the trader comes out to be Rs. 8000/-.

Now consider another case,

• CASE 2:  The farmer sells the cow to his brother at Rs.12000, now the selling price of the previous transaction becomes the cost price of this transaction, since the seller and buyer have changed. Now CP here is Rs.10000.

So what we conclude is that we need to first chalk out the transaction that is being discussed before advancing towards any calculations.

Students, we would be analyzing the underlying concepts rather than relying on ready-made formulae, so that we could solve any problem related to this topic, and at the end of all this concept building, you would be in a position to write all the formulas on you own.

Just remember basic things like, if SP is greater that means profit is made, and if CP is greater than SP, loss is incurred.

Also, profit % or loss % would always be calculated by keeping CP as reference, as evident from the previous statement.

• This unit requires just basic arithmetic and knowledge of percentage to cover entire concepts.

Let’s take an example and understand all the concepts one by one.

• Ex.1.) A boy sells his bicycle at Rs.600, and in this situation he gains 20%. Calculate profit, CP and SP.

Ans.) Here we have a situation in which a boy is selling his bicycle, (Businessman in making!). Okay, so coming to the problem now,

We get the selling price that is given in the question itself, i.e. Rs.600.

Now, as stated earlier we need to focus on the transaction involved, upon selling the bicycle at Rs.600, he gains 20%, so we get an idea that the SP is 20% more than the CP. So, we easily calculate CP as Rs.500, and profit as Rs.100.

Till now, we have not discussed any formulae, rather solely relied on concepts and analysis of transactions involved.

• Ex.2.) Ram purchased a TV at Rs.12000, and sold it at Rs.15000, find the loss or profit involved.

Ans.) Here, we have the purchase price, that is the CP = Rs.12000, also the selling price is 15000, so we see that the SP > CP, therefore we have profit involved here.

So, profit would be how higher the SP is than CP, so we get ,

Profit = SP-CP.

So, Profit = 15000-12000= 3000

Now, bonus question, lets calculate profit % here, for that again concepts come into play, since profit is calculate by keeping the CP as the reference, therefore for calculating Profit %, we need to take CP as reference again and calculate that how much % more is SP than CP or in more  simpler terms, Profit is what % of CP. Task done!!!!

So, Profit % = (Profit/CP)x100

OR Profit % = ((SP-CP)/CP)x100

Now, calculate.

• Now, coming to the last two topics left, and as the customary approach that we have been following, I would be again telling you a story for perfect visualization.

• So, you visit a shopping complex and see your favorite watch out there, now you see the label on it that states Rs.4000. Now, the salesman approaches you and starts telling you about the functions of it, but what is more important is the discount about which he tells you would be provided, being 25%. You find the deal nice and buy it.

Now, from the above case, we deduce that the MP of the watch is Rs.4000, and the discount provided is 25%.

Since discount is provided over the MP so, we calculate the value of discount as 25% of MP, i.e. Rs.1000.

And we get the SP as MP-Discount = Rs.3000.

NOTE: Since discount is provided on MP, therefore for calculating discount, using discount%, we would always use MP as the reference. As was the case with Profit or Loss %, in which we used CP as the reference.

Let’s take a quick example to brush up the concepts discussed.

• Ex.1) The price of one banana is Rs.5, Ram buys two dozens ,when told that he would be getting a discount of Rs.6 per dozen of the bananas bought. Find the price Ram needs to pay and the discount % provided.

Ans.) Here we see that one banana costs Rs.5, so for 24 bananas, Ram needs to pay Rs.24×5 = Rs.120. But, for each dozen he gets a discount of Rs.6, so the net discount comes out to be = Rs.12.

Therefore, the SP comes out to be Rs.120-12= Rs.108 (This is the amount Ram needs to pay to get 2 dozen bananas).

Now, for discount %, as discussed earlier, we need to consider MP as the reference value for calculating the same. So, discount % = (Discount/MP) x100. Which comes out to be: (12/120) x100 = 10%.

• Everything discussed above employs only basic aptitude and the concepts underlying these terms. Having said that, it could be inferred now that we are in a position to work out any problem given to us.

But before jumping to that, I would like out teams to come up and write all the formulas of the terms discussed till now. Write as much formulas as you can, by just recalling the basic definitions of the terms, and let’s see how the concepts work wonders for us. It is always the concept that derived the formula, so focus on the basics and concepts!

• Here are the formulas, just for reference,

 Profit or Gain = Selling price – Cost Price Loss = Cost Price – Selling Price Profit percentage = (Profit /Cost Price) x 100 Loss percentage = (Loss / Cost price) x 100
• When discount is given,

 SP= MP-Discount Discount % = (Discount/MP)X100 Discount % = ((MP-SP)/MP)x100

30

Minutes

 Section 2: Foundation: By selling a watch for Rs.495, a shopkeeper incurs a loss of 10%. Find the cost of the watch for the shopkeeper. 2.)  A man sells his scooter for Rs.5000, after gaining a profit of Rs.1000. Find:         i.) CP,         ii.) Profit % 3.)  On selling 100 bicycles the retailer earns Rs.240000. Also he books a profit of         Rs.40000. Find the cost of each bicycle. 4.)  The shopkeeper marks his goods at Rs.100 each. Also, a discount of 20% is provided at the store. What amount needs to be paid to buy two items from the store? Section 3: Moderate: 1.) A shopkeeper sold his goods at Rs.2500 and made a profit of 25% in the process. Find his profit % if he had sold the goods at Rs.2200. 2.) The cost price of 50 mangoes is equal to the selling price of 40 mangoes. Find the profit or loss %. 3.) Anil bought an article at Rs.200 and sold it at a profit of 10%. What would be the increase in profit % if it was sold at Rs.230? 4.) Aman sells his brand new watch marked at Rs.5000, to his friend and gains Rs.500, despite providing a discount of 10%. Find the price Aman had paid while buying the watch for him. Section 4:HOTS – HIGH ORDER THINKING SKILLS: 1.) A merchant sells two puppies at the same price; on one he makes a profit of 20%, whereas he incurs a loss of 20% on the other. Find his loss or gain % on the whole transaction. 2.) The MP of a table is Rs.1200, which is 20% above the cost price. If it is sold at a discount of 10%. Find the profit %. 3.) What price should a shopkeeper mark his goods, costing him Rs.153, to gain 20% after allowing a discount of 15%? 8 minutes  1.)Rs.550  2.)i.)Rs.4000      ii.) 20%  3.) Rs.2000  4.) Rs.160 10 minutes 1.)10% 2.)25% profit 3.) 5% 4    4.)Rs.4000 15 Minutes 1.) 4% 2.) 8 3.) Rs.216 Exp Time 10 minutes 10nu Closing Activity: Thank you everyone! Now, all of you are clear with your concepts of Profit and Loss. 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. We hope after today’s session you gain only profit in your life and never come across loss. 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. 1 minute Post -session