# Mathematics Study Notes on Profit & Loss

By Karishma Singh|Updated : October 13th, 2022

Today we will be covering a very important topic from the mathematics section which is Profit and loss. These formulas and shortcuts will be helpful for your upcoming Exams like KVS, NVS, CTET & TET Exams. If you like it let us know.

## Cost Price:

The price, at which an article is purchased, is called its cost price, abbreviated as C.P.

## Selling Price:

The price, at which an article is sold, is called its selling price, abbreviated as S.P.

• Profit/gain = SP – CP
• Profit % = Profit/(CP)×100
• SP = (100+gain % )/100  ×C P
• CP = 100/(100+gain %)×S P

Loss:

If the overall Cost Price exceeds the selling price of the buyer then he is said to have incurred a loss.

• Loss = C P – S P
• Loss % = LOSS/(CP)×100
• SP = (100-loss %)/100×C P
• CP = 100/(100-loss %)×S P

## Profit and Loss Based on Cost Price

To find the per cent gain or loss, divide the amount gained or lost by the cost and multiply it by 100.

Example: A toy that cost 80 rupees is sold at a profit of 20 rupees. Find the per cent or rate of profit.

Gain/cost × 100 = % profit.

20/80 × 100 = 25%. - Answer

To find the loss and the selling price when the cost and the per cent loss are given, multiply the cost by the per cent and subtract the product from the cost.

Example: A damaged chair that cost Rs.110 was sold at a loss of 10%. Find the loss and the selling price.

Cost x percent loss = loss.

110 x 1/10 = 11, loss.

Cost - loss = selling price.

110 - 11 = 99, selling price.

## Profit and Loss Based on Selling Price

To find the profit and the cost when the selling price and the per cent profit are given, multiply the selling price by the per cent profit and subtract the result from the selling price.

Example: A toy is sold for Rs. 6.00 at a profit of 25% of the selling price. Separate this selling price into cost and profit.

Selling price x % profit = profit.

Selling price = profit + cost.

6.00 x .25 = 1.50, profit.

6.00 - 1.50 = 4.50, cost.

To find the loss and the cost when the selling price and the per cent loss are given, multiply the selling price by the per cent loss and subtract the result from the selling price.

Example: At a sale, neckties selling at Rs. 50.00 are sold at a loss of 60% of the selling price. What are the loss and the original cost?

Selling price x % loss = loss.

Selling price + loss = cost.

50.00 x .60 = 30.00, loss.

50.00 - 30.00 = 20.00, cost.

To find the selling price when the cost and the per cent loss are given, add the per cent loss to 100% and divide the cost by this sum.

Example: Socks that cost 7.00 per pair were sold at a loss of 25% of the selling price. What was the selling price?

Answer: Cost / (100% + % loss) = selling price.

7.00 / 1.25 = 5.60, selling price.

To find the selling price when the profit and the per cent profit are given, or to find the selling price when the loss and the per cent loss are given, divide the profit or loss by the per cent profit or loss.

Note: This rule should be compared with the one under Profit and Loss Based on Cost. The two rules are exactly similar except that in one case 100% represents cost while in the other case 100% represents the selling price.

Example: A kind of tape is selling at a profit of 12% of the selling price, equal to 18 per yard. What is the selling price of the tape?

Answer: Profit / % profit = selling price.

18 /.12 = 1.50 selling price.

To find the per cent profit or loss, divide the amount gained or lost by the selling price.

Example: A candy bar sells for 1.30 at a profit of 65. What per cent of the profit on the selling price does this represent?

Answer: Gain / selling price = % profit.

65 / 1.30 = .5 or 50% profit.

Mark-up Price

Generally, if the SP is less than the marked price (MP) the difference between MP – SP is known as the discount, D.

Discount = M P – S P

Discount %, D% = (Discount) / (MP) ×100

To reduce per cent loss on the cost by per cent loss on the selling price, divide per cent loss on the cost by 100% minus per cent loss on cost.

Example: 20% loss on cost is what per cent loss on selling price?

% loss on cost / (100% - % loss on cost) = % loss on selling price.

0.20 / 80 = .0025 or 25% loss on selling price

To reduce per cent loss on the selling price to per cent loss on cost, divide per cent loss on the selling price by 100% plus per cent loss.

Example: 20% loss on selling price is what per cent loss on cost?

% loss on selling price / (100% + % loss on selling price) = % loss on cost.

.20 / 1.20 = .16666 or .16.67% loss on cost.

To reduce per cent markup (per cent profit on cost) to per cent profit on selling price, divide per cent markup by 100% plus per cent markup.

Example: A coat marked up 60% carries what per cent of the profit on the selling price?

Answer : % profit on cost / ( 100% + % profit on cost ) = % profit on selling price.

.60 / 1.60 = .375 or 37.5% on selling price.

### Here we are providing you with all the types of questions that have been asked in SSC Exams and How to solve them Easily with BEP methods:

Type 1:

The cost price of 40 articles is the same as the selling price of 25 articles. Find the gain per cent.

(a) 65%

(b) 60%

(c) 15%

(d) 75%

=(40-25)/25×100

=15/25×100=60%

BEP method

In Above question We take x = 40 , y = 25

Then Gain % = (x –y) x 100/ y

Type2:

Bananas are bought at the rate of 6 for Rs. 5 and sold at the rate of 5 for Rs. 6. Profit per cent is:

(a) 36%

(b) 42%

(c) 44%

(d) 48%

Answer : (c) To avoid fraction, let the number of bananas bought

LCM of 5 and 6 = 30

CP of 30 bananas

= 5 x 5 = Rs. 25

SP of 30 Bananas = 6 x 6

= Rs. 36

Profit = Rs. (36-25) = Rs. 11

Profit %

= 11/25×100=44%

BEP Method

[(6 x 6 -5x 5)/ (5 x 5)] x 100 = 44%

Type 3:

A man bought oranges at the rate of 8 for Rs 34 and sold them at the rate of 12 for Rs. 57. How many oranges should be sold to earn a net profit of Rs 45?

(a) 90

(b) 100

(c) 135

(d) 150

Answers: (a) Let the man buy 24 (LCM of 8 and 12) oranges.

C.P. of 24 oranges  = 34/8  ×24 = Rs. 102

S.P. of 24 oranges = 27/12×24=  Rs. 114

Gain = 114 – 102 = Rs. 12

Rs. 12 = 24 oranges

Rs. 45 =  24/12×45= 90 oranges

Type 4:

A shopkeeper earns a profit of 12% on selling a book at a 10% discount on printed price. The ratio of the cost price to the printed price of the book is?

(a) 45: 56

(b) 50: 61

(c) 90: 97

(d) 99: 125

Answer:  (a) C.P. of the book = Rs. x

Printed price = Rs. y

(y×90)/100=x × 112/100

x/y=90/112=45/56

Type 5:

A dealer sold two types of goods for Rs 10,000 each. On one of them, he lost 20% and on the other, he gained 20%. His gain or loss per cent in the entire transaction was

(a) 2% loss

(b) 2% gain

(c) 4% gain

(d) 4% loss

Answers: (d) Here, S.P. is the same, Hence there is always a loss. Loss per cent =(20×20)/100=4%

BEP Trick

Loss % = (n^2)/100= (20)^2/100= 4%

Where n= 20

Type 6:

On selling an article for Rs170, a shopkeeper loses 15%. To gain 20%, he must sell that article at rupees:

(a) 215.50

(b) 212.50

(c) 240

(d) 210

Answer: (c) C.P. of article = (200×120)/100 = Rs. 240

Type 7:

An article is sold at a loss of 10%. Had it been sold for Rs. 9 more, there would have been a gain of 12 1/2% on it. The cost price of the article is

(a) Rs. 40

(b) Rs. 45

(c) Rs. 50

(d) Rs. 35

Answers: (a) Let the cost price of the article = Rs. x

S.P. at 10% loss

= x×90/100= Rs. 9x/10

P. at 12 1/2 % gain

x  × (100+12 1/2)/100 = Rs. 225x/200

According to the question

9x/10 + 9 = 225x/200

180x + 1800 = 225x

x = Rs. 40

Type 8:

A sells a suitcase to B at 10% profit. B sells it to C at 30% profit. If C pays Rs 2860 for it, then the price at which a bought it is

(a) 1000

(b) 1600

(c) 2000

(d)  2500

Answer:  (c) If the C.P. of the suitcase for A be Rs. x, then

x ×110/100×130/100=2860

x=(2860×100×100)/(110×130) = Rs. 2000

Type 9:

Arun marks up the computer he is selling by 20% profit and sells them at a discount of 15%. Arun’s net gain percentage is

(a) 4

(b) 2

(c) 3.5

(d) 2.5

BEP method:

r1 = 20 , r2 = 15

Formula = r1 – r2 – (r1 x r2)/100

(20-15-(20×15)/100)

= 20 -18 = 2%

Type10:

A tradesman sold an article at a loss of 20%. If the selling price had been increased by Rs. 100, there would have been a gain of 5%. The cost price of the article was:

(a) Rs. 200

(b) Rs. 25

(c) Rs. 400

(d) Rs. 250

Answer  (c) Let the C.P. of the article be Rs. x.

105% of x - 80% of x = Rx. 100

25% of x = Rx. 100

x = Rs. (100×100)/25

= Rs. 400

That’s how Profit and loss questions are solved easily.  Here is a shortcut quiz for profit and loss to test your practice.

Thanks