Transcript
00:00 Hello, my name is Oyase. Sunday. I will be taking you mathematics JSS2 class. We're looking at an interesting topic for today.
00:20 The topic is transaction in the home and offices. Transaction in the home and offices, we're going to be looking at it in two parts.
00:29 So, we're going to be having a Series 1 and a Series 2 class. So, what the class would be specially designed for Series 1.
00:37 So, on that, the Series 1, we have the specific objective that the class is expected to achieve.
00:43 Now, what are our objectives for the Series 1?
00:47 The objective is able to solve simple commercial arithmetic relating to profits, interest, discount and commission.
00:59 How do you walk around commercial arithmetic relating to profits, interest, discount and commission?
01:09 That's the focus of the class. So, we begin each of them and we're taking look at them one after the other.
01:17 Now, starting off with profits. A profit for profit or loss. So, you either make profits and you have loss.
01:30 For profit and loss, we have the following concepts as to be looked at. Look at the cost price.
01:40 Look at selling price. Now, the cost price, the selling price. We're considering profit and loss.
01:52 And when profit and loss, we take a look at three elements. We have the first box, the second box and the third box.
02:03 So, we have the markets, the M, the trader, C and the final consumer, C.
02:10 But how do these three relates? How do they relate when they come to commercial arithmetic?
02:15 The cost price is the price that the trader pays when she buys an item, including every other amount that is used up in the process.
02:26 So, the trader goes to the market. The private amount he pays to get the product is called the cost price.
02:35 Now, the selling price, the price to be the trader sells to the item to the consumer. The trader sells the item to the consumer.
02:45 That becomes the selling price. So, you can see. So, the trader becomes the intermediary.
02:52 So, the trader has two options. The trader could have that profit or the trader can make a loss.
02:58 So, we are centred around the trader. So, we have the difference between the cost and the selling price is the profit.
03:06 I said, the relationship between the cost price and the selling price gives you your profit or your loss.
03:13 If the selling price is greater than the cost price, you have profit.
03:18 But if the cost price is greater than the selling price, you have loss.
03:22 If the selling price is more than the cost price, it is profit. And if the selling price is less than the cost price, it's worth a loss.
03:30 So, if the trader goes to the market, now buy it and the selling price is more than is going to be making what profits.
03:42 But if the selling price is less than make what a loss.
03:46 The challenge we are going to be having here is, how do we now calculate the profit or loss in percentage?
03:55 Okay, we can determine the profit, but how do we calculate it in percentage?
03:59 There will be a need for us to put the profit or the loss in percentage.
04:03 So, the profit or profit or profit would give us, we have selling price x minus cost price.
04:14 So, we believe that the selling price is greater than the cost price, both putting it in percentage.
04:21 Putting in percentage will have the profits, the so-called profits or the loss that we have over the cost price.
04:31 As they see, they multiply by 100 in percentage.
04:37 Now, did that simply give you an idea of what to do?
04:41 This is when the profit or loss percentage is unknown.
04:44 As the profit or loss percentage is unknown, you follow to this method.
04:49 But there might be some other questions where the profit or loss percentage will give you the projected percentage of profit or loss.
04:56 Now, when they do that, we would have to reverse this formula the other way around.
05:01 So, let's pick a question from this.
05:04 For example, one says, a trader buys 50, 1 litre carton of drinking yogurt from a factory.
05:13 The yogurt would take very well.
05:15 Now, it pays 550 per 1, for 1 litre of the carton.
05:20 It pays 550.
05:21 On the way to the store room, 8 cartons are burnt open.
05:27 And the yogurt spills out.
05:29 It's already out.
05:31 Now, the trader sells the remaining carton at 600 each.
05:36 Calculate its percentage profit or loss.
05:41 How much did he buy?
05:43 55.
05:44 That is 5.15.
05:47 How much did he sell?
05:49 600.
05:50 Now, the final is, what is the cost?
05:53 First, determine the cost.
05:57 Now, we have...
05:59 Example 1.
06:00 What is the cost?
06:01 The cost price.
06:03 The cost price is 55.
06:08 550.000.
06:09 550.000.
06:10 Multiplied by how many did he buy?
06:14 But 50.
06:15 Techniques.
06:16 So, the first thing you write out all the parameters that are given.
06:20 So, it's easy.
06:21 Parameters are given already now.
06:23 Then it's easy to compute.
06:25 So, we have 550 times 50 does 27.500 is the cost price.
06:35 Now, when to calculate the selling price?
06:39 How much did he sell?
06:41 Selling price.
06:43 Now, the selling price is, but before we get the selling price, there's a need.
06:48 Six, eight of them.
06:50 Look at it.
06:51 They were eight.
06:52 They were both open and to a speed.
06:55 So, we're going to subtract the eight out of the 50.
06:58 So, we're going to be able to determine how many did we...
07:01 Did he finally sell?
07:03 So, to get the selling is selling at 50 minus eight.
07:10 So, it's going to be selling our one.
07:13 42 cartons.
07:15 It's selling for two cartons.
07:17 So, what would not be the selling price at 42 cartons?
07:21 Because selling price gives us 42 times 600.
07:28 And for two times 600 does give us 25,200.
07:37 Now, what we need to do in the first place is compare.
07:40 This is the cost price.
07:43 And this is the selling price.
07:46 Compare the two.
07:48 Remember, the cost price, the selling price.
07:51 Compare the two.
07:52 Now, is it going to be making a profit or make a loss?
07:55 Look at it.
07:56 You see that this cost price is greater than the selling price.
07:59 And it would be at a loss himself.
08:02 How the...
08:03 You got speeded.
08:05 That's why in selling, the trader has to be very careful.
08:09 So, looking at it, we'll move up.
08:11 And...
08:13 We're happy with us.
08:14 The profit or loss.
08:16 So, the...
08:17 We said it's going to make a loss because it costs.
08:20 So, the loss we give us, what do we have?
08:22 We have what?
08:24 25 because 25,200 minus 27,500.
08:31 It's supposed to be a negative, but we know it's a loss.
08:35 So, we have...
08:39 Niagara sign of 2,300 is his loss.
08:43 This made it a loss.
08:45 So, now, express it in percentage.
08:48 That's the next step.
08:49 So, expressing this in percentage simply means you're going to be saying
08:54 the loss percentage, remember, is the loss.
08:58 What do you have at the loss?
08:59 That's 2,300 over.
09:01 What is the cost price?
09:03 That's 27,500.
09:05 Multiply by 100%.
09:08 So, the loss is expected to make.
09:11 Take this, take this out.
09:12 Take this, take this out.
09:13 Multiply them, you're going to be having 8.36%.
09:20 It's making a loss of 8.36%.
09:24 That's not much, but it could really affect the business to have
09:28 make a loss of 8.36%, with 2%, 3%, 4%, as 8% is really much.
09:35 So, that is how to determine your profit.
09:38 If it's to make a profit, oh, good and fine.
09:41 Now, the question is, now we have the selling price.
09:44 We have been to the selling price.
09:46 We have been to the cost price and we could just find the percentage.
09:49 What if you had a projected profit?
09:52 Oh, a projected profit percentage.
09:54 Okay, in the next transaction is projecting a 20% profit.
09:59 What would not be the selling price of that product or the cost price?
10:03 So, for that, we're having a different formula,
10:07 it's still a manipulation of the original formula.
10:11 If we look for the cost price, being given the profit percentage,
10:14 is the selling price multiplied by 100 over 100 plus the profit percentage,
10:20 meaning that we're expressed that error would be expressive 100.
10:25 Both for the loss, we believe that it's making a loss.
10:28 So, there's some subtraction.
10:29 That's 100 minus the loss percentage.
10:32 Then, if it's the selling price, the reverse,
10:35 the reverse will only be that for the formula,
10:39 it's just going to be that the cost price that you're looking for,
10:43 that Cp will give us the selling price that SP is SP multiplied by 100 over 100 plus profit percentage.
10:59 That's P.
11:00 So, either the formula you apply depends on what the question is actually to look for.
11:06 Pick up the first question, question number two.
11:09 Esella buys 20 pair of women's sneakers from manufacturer, 20 pair, 10-minute, 20.
11:17 One of the pair gets damaged as they truck,
11:21 which the shoes is unlocked.
11:24 Now, you mean those trucks when taking the shoes or taking the sneakers from where they manufactured to the Trader's location,
11:33 one of them got damaged.
11:34 Now, the Trader decided to sell this pair at a lower price of $7,000.
11:41 The loss is projected to be 20%.
11:44 Now, look at it.
11:46 We don't know the cost price.
11:48 How much it buys the 20 pairs?
11:51 But one of the pair that got damaged was sold at a lower cost of what, $7,000.
11:59 And we said it's making the loss percentage of 20%.
12:03 Now, what would be the calculated cost price for this pair of sneakers?
12:08 The question is pick out your variables.
12:11 It's very important that before you start solving any mathematical question pick out the variables that are given.
12:16 So, we have the cost price represents 100%.
12:21 We don't know, say, example 2.
12:23 Cost price is at 100%.
12:30 So, we have a loss was made on the cost price.
12:33 And what was the loss?
12:34 So, we are trying to project that the selling price was made in loss.
12:39 So, the selling price would be at the loss percentage.
12:43 So, we are having the selling price to give us 100%.
12:48 If it was a profit that they made, I would have added it, but they made a loss.
12:52 So, they made a loss.
12:53 So, 200% minus what was lost?
12:57 20%.
12:58 So, we are projecting that it was an 80% that the selling price should have been since it made a loss.
13:08 If it was a profit, it would have been a 120% if it's a profit, but because it's a loss, we have 80%.
13:14 Now, the cost price, the cost price would give us what the selling.
13:22 The selling is a sold one that we don't got at 7000, multiplied by 100 over 100 minus what was the percentage of the loss?
13:36 It's already given at what 20%.
13:41 So, I will have it as a projected cost by that Cp will give me 7000 multiplied by 100 over 100 minus 20.
13:55 That would give me 80. So, when I do my calculation, I would be having that my price will be 8000,
14:11 7500, is the cost price for each of the items at a loss of 20%.
14:22 It gives you an idea and it's okay, the loss percentage is given.
14:25 If it was in a profit, you remember it would be an addition.
14:30 If you looking for the selling price, it would be a reversal.
14:34 So, take note of how the manipulation has been done and what is given.
14:38 The first, like I said, pick out the parameters and it is easier to go to the process.
14:43 So, I have interest. The next, the next on our list, collection of lists, is interest.
14:47 Interest is an extra money you pay on the loan or money you earn on an investment.
14:53 The money you pay on the loan or you earn on an investment is called interest.
15:00 Now, a loan is an amount of money you borrow. When you borrow money, they call it a loan.
15:06 Boy, that you most normally pay back with interest. You pay back a loan.
15:12 You take a loan. You take a loan from your bank. You take a loan from individuals.
15:17 You take a loan from corporate organizations. You take a loan.
15:20 This is money you take, maybe for an investment purpose.
15:23 So, you take a loan or I'm taking up this loan to be able to finance this investment.
15:27 Oh, I want to build this company and I need a money.
15:31 So, you go to the bank or go to the corporate bodies that give you huge amount of money.
15:35 You start off a company. That is called what we call a loan into an investment.
15:41 An investment is an amount of money you give to an business or bank.
15:48 In the hope of getting more money back, you get that.
15:52 So, when there is a loan, there is an investment, there is going to be an interest.
15:56 So, looking at the relationship between the three.
15:58 Now, looking at it, there are three boxes again on that interest.
16:04 Remember, on that, we have three boxes again. These are three boxes.
16:08 And what connects them? There are three boxes.
16:12 And they have the bank or whatever it is that I want to approach for the loan.
16:19 I have the person, which is the individual who wants to take the loan.
16:23 I have what I want to do with the loan, where the company who takes the loan.
16:28 Now, the bank gives a loan. What the bank gives a loan?
16:33 The loan is given. That's the loan.
16:36 And the loan is used for investment. That's investment proposed.
16:41 Now, when you use for investment proposed, at the end of the day,
16:46 is expected to pay something back for the loan.
16:49 And that is called your interest.
16:53 So, you're expected to get pay back.
16:56 So, the relationship between the loan investment is called the interest.
17:00 So, we usually call it the interest, which is called the simple interest.
17:04 And the simple interest is the principal, that the money you borrow or the money you took,
17:11 times the interest rates, at which the bank is giving you the money.
17:15 Multiply by the time, the amount of time, the time duration of paying back.
17:21 I would just say my simple interest is principal, times, my interest rate, time, the number of years I want to use it.
17:31 But the actual amount that I'm to pay back would simply be my principal,
17:36 close the interest that I'm paying, the interest I want to pay, close the interest and paying.
17:42 So, when I bring up the entire equation, I will have, what's my simple interest?
17:48 That would give me PII, multiplied by I, multiplied by N.
17:56 So, at the end of the day, my amount that I'm expected to pay, at the end of the duration,
18:04 whether it's five years, three years or four years, the amount I'm expected to pay would be P,
18:09 open bracket, one, close, I, N, N. So, work around it.
18:16 Now, let's pick a question.
18:18 A man invested 60,000 in a fixed deposit account with an interest rate of 8% per annum.
18:27 Calculate the interest in after five years, as well as the balance of the account at the end of five years.
18:36 What happens is, like I said, you could put the money into an investment.
18:40 So, this man's theory is okay.
18:42 I cannot use this money.
18:44 Now, for the next five years, I shoot.
18:47 And also, the money, money is expected to yield a certain percentage of interest every year,
18:55 due to the value of inflation.
18:58 Meaning that 10,000, in two, three years from now, would depreciate in value.
19:04 So, that is the reason why interest comes in.
19:06 So, this man invested 60,000 in a fixed deposit account.
19:11 And every year is given 8% per annum interest and is projecting five years.
19:18 So, after five years, what will be the amount that is going to have?
19:23 Simple.
19:25 Follow your computation to the process.
19:27 Just know how to fix them in.
19:29 So, I have solution.
19:32 That's a solution.
19:35 And I have, how much was invested, principal invested, 60,000?
19:44 At what interest rate?
19:46 Interest rate does I at 8% interest rate?
19:50 And I have many numbers of years at 5%.
19:53 So, what are you looking for?
19:55 You're looking for the interest of that working rate.
19:58 So, my interest, that's my simple interest, will give me what's my principal?
20:03 That's 60,000.
20:06 Multiply by what the interest rate does 8% to over 100.
20:12 Multiply by what the time that's five years.
20:15 So, take it up.
20:19 Interest will give me, that will give me 60,000 times five.
20:25 That gives me what?
20:27 300,000.
20:30 Multiply by 8% over 100.
20:35 So, this goes for this and this.
20:40 The will have our interest would give me 24,000.
20:47 Now, after five years, the interest accumulated will be what?
20:53 24,000.
20:54 If you want to determine how much five years, you just divide it 24,000 by five.
20:59 So, how much, into about after five years, the interest accumulated will be what?
21:04 24,000.
21:05 It will now be the amount after five years.
21:09 So, the amount will now be that after five years, I'm going to be having my amount.
21:15 It will now be what my principal, initial amount invested.
21:19 60,000.
21:21 Plus, what's my interest for the community period?
21:24 24,000.
21:26 Where you add them up together, I will have it as what?
21:29 84,000.
21:30 So, after five years, 60,000 result into 84,000.
21:37 That's a good investment.
21:39 But if 60,000 error is kept somewhere under the bed or somewhere else, without being used
21:45 for investment purposes, it will only remain at 60,000 error would never change.
21:50 But when my investment proposed, it is also how we have accumulated what?
21:57 This is the 84,000.
21:58 Now, moving to the third part.
21:59 We just have the fourth part we're looking at.
22:01 The third part is this discount.
22:03 In a home, you can give discount.
22:05 It's the reduction in the market price of an item.
22:09 So that the customer pays less than the normal price for the item.
22:13 Trade does often give the discount when customer pays cash instead of buying on credit.
22:19 And they may also give you a discount when customer buys in large quantities.
22:23 So, discounts are given to customers who buy in large quantity.
22:27 Oh, you purchase in large quantity.
22:29 The buyer or the trader is happy, gives you a discount.
22:33 Now, remember, gives you a discount.
22:36 So, all you pay promptly, you don't want to buy on credit if you are paying promptly.
22:40 The trader or the buyer can decide to also give you a discount.
22:44 So, discount can go either in the time where you buy in large quantity or you pay promptly.
22:50 So, at that point, give up your discount.
22:53 So, discount percentage is unknown.
22:55 That is a process where a discount percentage is unknown.
22:59 So, if the discount percentage is unknown, we expect that the discount discount percentage is unknown.
23:08 So, the discount, which is D, will be your normal price, that the normal price minus your discounted price.
23:15 So, we get our discount.
23:17 But, if you are not expressing it in percentage, if you are expressing it in percentage,
23:23 that's the expressing your discount in percentage.
23:25 It will give us the discount that the one you've gotten above over the normal price,
23:32 that the normal price of the product, normal price.
23:37 Then, express in 100%.
23:41 This one is, we are trying to get the percentage because the percentage is unknown.
23:46 So, pick the question.
23:47 It's from a kid who has too much stock of a certain brand of a big faster cellular.
23:54 The manager decides to sell the 350 gram box that are normally priced at 180 for 1,000,
24:05 6, 5, 6.
24:08 A normal price was to be to be 1,800.
24:11 But, the manager decides to sell because they have so much stock.
24:16 So, to attract customer to buy, we bring down the price.
24:20 Bringing down the price is discount.
24:22 Now, at 1,656, calculate the percentage discount per box.
24:29 So, because we now have more people who wants to buy, or want to buy because the price has been slashed.
24:34 First, what do you do?
24:37 First, what is the normal price?
24:40 So, to be able to get your discount, that's the example 4, to get your discount, what is discount?
24:49 First, what is the normal price?
24:50 Normal price is 1,800.
24:53 How much was this sold for?
24:55 1,656.
24:58 So, your discount is 144 per box.
25:04 So, anyone who buys per box is going to be given 144.
25:08 Now, what would not be the percentage of the discount?
25:11 The percentage of the discount would give us the discount, which is 144 over what is the normal price of the product?
25:18 The normal price is 1,800 times 100%.
25:24 Now, that gives me 8% discount.
25:29 8% discount.
25:30 You will be able, you know, if you watch your TV very well, you will be able to say, "Oh, I'm giving 8% discount to buy this commodity."
25:38 So, 8% discount is taken of the percentage from the amount.
25:43 But sometimes, also, the percentage might be known, like I just said.
25:48 Oh, we are selling this phone at 25% discount.
25:53 So, you don't ask yourself, "How do I get up the discount from the price?"
25:59 So, the normal price will be equal to your discounted price, multiplied by 100.
26:04 All of our 100 minus the discount.
26:07 They are expected that the discount price or your popularity for the discount price.
26:12 So, if you are a popularity for the normal price or the discount price, the two formulas are this.
26:18 100 divided by 100 minus discount or 100 minus discount divided by 100.
26:25 Now, picking the question, question number 5.
26:27 It said, "It's for market offers 5% discount if a customer buys more than 20 sub-drink in 33 liters of current."
26:37 33 liters of current that if you buy more than 20, you will be given 5% discount.
26:43 A customer or a consumer buys how many? 24.
26:49 And pays 3420.
26:53 Calculate the normal price, parking.
26:57 Now, it is paying.
27:00 Going fully well, just look at it carefully.
27:03 Looking at it, what do we have?
27:05 The discounted price.
27:06 We expect that the discounted price, example 5, the discounted price, the discounted price.
27:12 It's always at 100 percent.
27:15 So, we have been given 5% discount out.
27:19 So, we are expected to have a 95% discounted price.
27:23 So, when we have that, what is e?
27:26 We now have a normal price.
27:28 Remember, a normal price, a normal price, a normal price.
27:34 What give us what we have?
27:38 3420.
27:42 Remember your 3420.
27:44 3420, that's the discounted price.
27:48 Multiply by 100 over 100 minus 5.
27:56 So, that gives me a normal price.
28:00 That gives me 3420.
28:04 Multiply by 100 over 95.
28:09 So, my normal price of it gives me a much 3600 in the normal price.
28:17 So, at a 5% discount given, you are having that, that's the discount given.
28:22 That's why the price.
28:23 I'll decide to go to 4000, 3000, 420.
28:27 Because of your 5% discount.
28:30 Now, the last aspect is the commission.
28:33 That's the money that an agent pays to perform a service.
28:38 Commission.
28:39 The money an agent pays to perform a service.
28:42 When you perform a service, you have been paid a commission.
28:45 Lawyers, salesmen, insurance, they have been paid for a commission.
28:50 Now, the question is, how do you calculate your commission received?
28:53 When you have your commission, how do you calculate your commission received?
28:56 Your commission received is commission to percentage multiplied by the values over the services.
29:02 And multiplied by 100.
29:04 That's commission received.
29:05 Or commission percentage is commission received over the values of sales multiplied by the services.
29:11 Now, these are how you get it.
29:14 Then, let's pick a question.
29:16 A salesman receives a basic salary of 85,000 and a commission of 15%.
29:21 It gets the commission of 15%.
29:23 It's basically a salary of 5,000.
29:25 But whenever it works, it gets a 15% commission on all sales are both 25,000.
29:31 So, when it sells about 25,000, it gets you 15%.
29:35 If the salesman are sold, stock, what's 60,000?
29:40 What is a two-tape for the month?
29:43 What's a two-tape for the month?
29:45 First, what's the commission an?
29:47 That's it.
29:50 What's the commission an?
29:52 The commission an?
29:54 That is the commission that the salesman an?
29:57 The commission an?
30:02 So, commission an is what?
30:05 We have, remember, 60,000 minus 25,000.
30:13 And the balance gives us what?
30:15 35,000.
30:17 That's the commission is, he has handphone for himself, for making the sales that is above that amount.
30:24 Now, what will be the commission received?
30:27 Or the commission that it would get at the end of the day?
30:30 The commission received, we're expressing it, that gives us what?
30:36 Remember, it's 15%.
30:38 That's 15 over 100.
30:41 Times the commission in N, that's 35,000.
30:45 And that gives us what?
30:47 5,000, 250.
30:50 Now, 5,000, 250.
30:53 What will that be?
30:54 It's total pay.
30:55 The total pay for the month.
30:57 Total pay for the entire duration would be its salary.
31:01 It's 5,000.
31:03 The 5,000 plus the commission gets 5,000 to 50.
31:08 And the total amount gives me 90,000 to 150.
31:14 Wow.
31:15 That's a huge amount of money when he has made a sales for the amount.
31:19 So, with this, it's giving you a very good idea on what to expect.
31:24 Remove to the evaluation.
31:26 Evaluation questions are questions I enable you to give you to solve.
31:29 Questions relating to what we've discussed.
31:32 And the evaluation sessions, a debt collector received 20% commission
31:36 on how money he manages to get from all debtors.
31:40 It gets 20%, 12% off it.
31:42 Capital, the commission receives on collection of 2,000, 46,000.
31:48 And questions about two sales calculate the total amount of money paid back after 5 years
31:53 on a loan of 25,000 with an interest rate of 15%.
31:58 Wow.
31:59 That's a good question.
32:00 Thank you very much for watching.
32:03 My name is Ayase Sunday.
32:05 Till next time.