In profit and loss, the activity of buying things from one place and selling them at another place is known as business.
Explanation I:
Sam is a shopkeeper. He buys the following articles from a wholesale market at the following rates:
Article
Water Bottle
Pen
Pencil Box
Lunch Box
Ball
Purchased at
$ 45
$ 10
$ 25
$ 30
$ 5
Sold at
$ 60
$ 25
$ 35
$ 55
$ 8
Rate at which an article is purchased is called Cost Price (C.P.)
Rate at which an article is sold is called Selling Price (S.P.)
Sam purchases the water bottle for $ 45. He sold it for $ 60.
Here, cost price = $ 45
Selling price = $ 60
Thus, earning $ 60 - $ 40 = $ 20 more
The extra money earned by selling an article is called profit or gain.
When Selling Price (S.P.) is greater than the Cost Price (C.P.) we have a gain (Profit).
Sam purchases the pencil box for $ 25. There were some defects in the pencil box.
So, he sold it for $ 20.
Here, Cost Price = $ 25
Selling Price = $ 20
Thus, lost $ 25 - $ 20 = $ 5
The money lost by selling an article is called Loss.
When Cost Price (C.P.) is greater than the Selling Price (S.P.) we have a loss.
Profit or Gain = S.P. - C.P. = Selling Price - Cost Price
Loss = C.P. - S.P. = Cost Price - Selling Price
Explanation II:
Ron is a shopkeeper. He buys his goods either from the factory directly
or from the whole seller. He then tries to sell each of goods or item at
a higher price to earn money. If he succeeds, he makes a profit or gain
or else he suffers a loss.
For example:
1. If Ron buys rice at $ 20 per kg and sells it at $ 23 per kg, he makes a profit of $ 3. (i.e., 23 - 20 = 3)
Cost price (CP) = $ 20,
Selling price (SP) = $ 23
Profit or Gain = $ 20
2. If Ron buys rice at $ 20 per kg and sells it at $ 18 per kg, he suffers a loss of $ 2 i.e., (20 – 18 = 2)
Cost price (CP) = $ 20,
Selling price (SP) = $ 18
Loss = $ 2
From this we understand:
(i) The price at which a man buys his goods is called the Cost Price (CP).
(ii) The price at which a man sells his goods is called the Selling Price (SP).
(iii) When the SP is greater than CP the man makes a Profit or Gain.
SP > CP → Profit = SP – CP
(iv) When the SP is less than CP the man suffers a Loss.
SP > CP → Loss = CP – SP
For example:
1. Ron bought rice worth $ 2000 and spent $ 200 for transporting it to his shop, $ 150 on getting it cleaned and $ 50 on packing.
Then total CP = 2000 + 200 + 150 + 50 = $ 2400.
(v)
Transportation charges, labour charges, salaries etc. are called
Overhead Expenses and these are always added to the cost price to get
the total CP.
More Examples on Profit and Loss:
1. Ron came home from school at 4 o’clock. Then his mother gave him a list.
Sugar = 1 kg
Electric bulbs = 2 nos.
Geometry box = 1
Ron goes to a provision store to buy sugar.
A provision store sells rice, wheat, soap, oil, etc.
He goes to an electrical shop to buy bulbs.
An electrical shop sells all electrical goods.
He goes to a stationery shop to buy geometry box.
A stationery shop sells paper, notebooks, pens, pencils, boxes, etc.
A person who sells goods in large quantities is called a whole sale dealer.
The person who sells small quantities of goods is called a retainer.
The retailer buys articles from whole sale dealer at a price. He adds a little extra money on each article and sells them to customers.
Cost price (CP):
The price at which the retailer buys the articles is called Cost price.
Selling price (SP):
The price at which the retailer sells the articles is called Selling price.
2. Suppose the retailer buys an article for $ 250 and he sells it for $ 285. Here $ 250 is called the cost price of the article and $ 285 is called the selling price of the article.
In this case, since the selling price is greater than the cost price, it is called profit.
The difference between selling price and cost price is called profit or gain.
S.P – C.P = Gain
S.P = C.P + Gain
C.P = S.P – Gain
3. Ashley bought IV standard Mathematics text for $ 50 last year. After studying she gave it to her friend for $ 25.
Here $ 50 is the cost price and $ 25 is the selling price.
In this case, since the cost price is more than the selling price, the difference between selling price and cost price is called loss.
C.P – S.P = Loss
C.P = S.P + Loss
S.P = C.P – Loss
4. Ron bought a grinder for $ 1500. He sold it for $ 1000. What is his gain or loss?
Cost price of a grinder (C.P) = $ 1500
Selling price of a grinder (S.P) = $ 1000
Since cost price > selling price; loss = cost price – selling price
= $ 1500 – 1000
= $ 500
Therefore, loss = $500.
5. Kate sold her cow for $ 3200. If she gained $ 290 find the cost price.
Selling price of cow (S.P) = $ 3200
Gain = $ 290
Cost price of the cow (C.P) = selling price – gain
= $ 3200 - 290
= $ 2910
Therefore, C.P = $2910.
6. A man bought a sofa set for $ 8250. He sold it at a loss of $ 500. Find the selling price.
Cost price of sofa set (C.P) = $ 8250
Loss = $ 500
Selling price of sofa set (S.P) = cost price – loss
= $ 8250 – 500
= $ 7750
Therefore, S.P = $ 7750
7. Amy bought a watch for a certain amount and sold it for $ 870. What is the cost of it, if it was sold at a loss of $ 125?
Selling price of the watch (SP) = $ 870
Loss = $ 125
Cost price of the watch (CP) = selling price + loss
= $ 870 + 125
= $ 995
Questions and Answers on Profit and Loss:
I. Complete the table:
C.P Rs. |
S.P Rs. |
Gain Rs. |
250 |
283 |
_____ |
_____ |
365 |
25 |
195 |
_____ |
30 |
1210 |
1250 |
_____ |
6650 |
_____ |
45 |
_____ |
576 |
19 |
II. Complete the table:
C.P Rs. |
S.P Rs. |
Loss Rs. |
456 |
420 |
_____ |
_____ |
629 |
28 |
392 |
_____ |
41 |
1545 |
1505 |
_____ |
6295 |
_____ |
250 |
_____ |
728 |
100 |
III. Worksheet on Word Problems on Profit and Loss:
Solve the following problems:
1. A shopkeeper purchased an article for $ 250 and sold it for $ 300. Find his gain.
2. Ron bought a two wheeler for $ 19200 and sold it at a loss of $ 1500. Find the selling price.
3. A farmer gained $ 350 by selling a goat for $ 3200. What is the cost price?
4. An article was bought for $ 5565 and was sold for $ 5220. Find the loss.
5. A person sold his house for $ 75000 and lost $ 15000 on it. Find the cost price.
6. A trader bought an article for $ 1275. By selling it he gained $ 350. What is the selling price.
To find Cost Price or Selling Price when Profit or Loss is given.
5th Grade Math Problems
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