# Profit and Loss

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.PRs. S.PRs. GainRs. 250 283 _____ _____ 365 25 195 _____ 30 1210 1250 _____ 6650 _____ 45 _____ 576 19

II. Complete the table:

 C.PRs. S.PRs. LossRs. 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.

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• ### Formulas of Profit and Loss | Profit and Loss Important Formulas

Formulas of profit and loss are given below. When the Selling Price (SP) is greater than Cost Price (CP) the man makes a Profit or Gain. Selling Price (SP) > Cost Price (CP) → Profit or Gain

Profit and Loss.

Formulas of Profit and Loss.

To find Cost Price or Selling Price when Profit or Loss is given.

Worksheet on Profit and Loss.