profit and loss

Black Holes of Aptitude-Profit and Loss

©Mayank [email protected],9990123477

Profit and Loss

What is Profit?

When a person does a business transaction and gets more than what he had invested, then he is said to have

profit. The profit he gets will be equal to the additional money he gets other than his investment. So profit can

be understood as the extra money one gets other than what he had invested.

Exp: A person bought an article for Rs. 140 and sold it for Rs. 120. Then he got Rs. 20 extra and so his profit is

Rs. 20.

What is Loss?

When a person gets an amount less than what he had invested, then he is said to have a loss. The loss will be

equal to the deficit he got than the investment.

Exp: A person bought an article at Rs. 100 and sold it for Rs. 90. Then he got a deficit of Rs. 10 and so his loss

is Rs. 10.

Cost Price (CP):

The money that the trader puts in his business is called Cost Price. The price at which the articles are bought is

called Cost Price. In other words, Cost Price is nothing but the investment in the business.

Selling Price (SP):

The price at which the articles are sold is called the Selling Price. The money that the trader gets from the

business is called Selling Price. In other words, Selling Price is nothing but the returns from a business.

Marked/Market/List Price (MP):

The price that a trader marks or lists his articles to is called the Marked Price.

This is the only price known to the customer.

Discount:

The waiver of cost from the Marked Price that the trader allows a customer is called Discount.

Profit or Gain:

If S.P. is greater than C.P., the seller is said to have a profit or gain.

Loss:

If S.P. is less than C.P., the seller is said to have incurred a loss.



Profit=P

Loss=L

S.P=Selling Price

C.P=Cost Price

M.P=Marked Price

Type I

Profit %= (𝑆.𝑃−𝐶.𝑃)

𝐶 .𝑃× 100

Loss% = (𝐶.𝑃−𝑆.𝑃)

𝐶.𝑃× 100

Profit and Loss will increase or decrease with quantity according to the number of item, but Profit and

Loss percentage will not vary with number of items.

Profit and Loss will always be calculated on Cost Price.

Exp.1: Farqui purchased a radio for Rs. 600, He sold it for Rs. 720.What is the percent profit he earned in the

transaction?

Solution:

P% = (𝑆.𝑃−𝐶.𝑃)

𝐶 .𝑃× 100

= (720−600)

600× 100

=20%

Type II: Golden Rule

𝑪. 𝑷 × 𝑭𝟏 = 𝑭𝟐 × 𝑴. 𝑷 = 𝑺.P

F1=Factor after profit/loss

F2=Factor after discount



How to calculate Factor

Let there is profit of 20 %, so F1 will be

100+20=120

120

100=1.2

Let there is discount of 3 % , so F2 will be

100-3=97

97

100 =0.97

How to calculate profit from factor:

If factor is less than 1 there will be a loss, if factor is greater than 1 there will be a profit.

Let there is Factor 1.2,so profit will be

1.2×100=120

120-100=20

So there will be profit of 20%

Let there is factor .97,so loss will be

0.97×100=97

97-100=-3

So there will be loss of 3%

Exp1: By Golden Rule

𝑪. 𝑷 × 𝑭𝟏 = 𝑺.P

𝟔𝟎𝟎 × 𝑭𝟏 = 𝟕𝟐𝟎

F1=1.20

So there will be 20 % profit.

Exp2: Atif purchased an article for Rs. 400 and sold it at 20% profit, find selling price?

Solution: 𝑪. 𝑷 × 𝑭𝟏 = 𝑺. 𝑷

𝟒𝟎𝟎 × 𝟏. 𝟐 = 𝑺. 𝑷

480=S.P



Exp3: Afeefa bought an article for Rs.1000, after getting a discount of 20 %, Find

Marked Price?

Solution 𝑭𝟐 × 𝑴. 𝑷 = 𝑺. 𝑷

𝟎. 𝟖 × 𝑴. 𝑷 = 𝟏𝟎𝟎𝟎

M.P=1250

Exp4: Nasir wants to earn 20% profit on an article after offering 25% discount to the customer if the cost price

of an item is 300, then the M.P of an article would be.

Solution: 𝑪. 𝑷 × 𝑭𝟏 = 𝑭𝟐 × 𝑴. 𝑷 = 𝑺.P

𝟑𝟎𝟎 × 𝟏. 𝟐 = 𝟎. 𝟕𝟓 × 𝑴. 𝑷

M.P=480

Type III

𝑃 = 𝑀 − 𝐷 − (𝑀×𝑑)

100P=profit %

M=Marked above Cost Price

D=Discount

Exp5: An article is marked 40 % above the cost price and a discount of 30 %is allowed, what is the gain or

loss percentage?

Solution: 𝑃 = 𝑀 − 𝐷 − (𝑀×𝑑)

100

𝑃 = 40 − 30 − (40 × 30)

100

= -2

So there will be 2% loss.

By golden rule

Let C.P=100x

𝑪. 𝑷 × 𝑭𝟏 = 𝑭𝟐 × 𝑴. 𝑷 = 𝑺

𝟏𝟎𝟎𝒙 × 𝑭𝟏 = 𝟎. 𝟕 × 𝟏𝟒𝟎𝒙

F1=0.98

So there will be 2 % loss.



Type IV

For increase in price

Original Price= (𝑟×𝑅𝑠.)

(100+𝑟)×𝑄

For decrease in Price

Original Price= (𝑟×𝑅𝑠.)

(100−𝑟)×𝑄

Exp 6: A 25% hike in the price of potato forces a person to purchase 2 kg less for Rs. 75.Find Original

Price.

Solution: Original Price= (𝑟×𝑅𝑠 .)

(100+𝑟)×𝑄

Original Price= (25×75)

(100+25)×2

=7.5

Exp 7: A reduction of 10 %in the price of salt enables a person to buy 2 kg more for Rs. 180.Find the

reduced and the original price/kg.

Solution: Original Price= (𝑟×𝑅𝑠 .)

(100−𝑟)×𝑄

Original Price= (10×180)

(100−10)×2

=10

Reduced Price =90% of 10

=9

Type V: If a person buys A goods for B and sells C goods for D, then the profit/loss % will be

Quantity and Rate Table

Make Quantity same by taking L.C.M and multiplying the appropriate number to the quantity.

Multiply the same number with Rs.

Find Profit /Loss

Direct Formula

Profit/loss %= (𝟏𝟎𝟎(𝐀𝐃−𝐁𝐂))

𝐁𝐂

Rs. =Rupee, r=rate, Q=Quantity



Exp 8: Salman purchased some lemons. He purchased 7 lemons for Rs. 9.He sold all

the lemons. If he sold 11 lemons for 13.Find Loss%.

Solution:

Step I: Take L.C.M of quantity (7, 11) =77

Step II: Make quantity equal by multiplying 11 and 7 in C.P and S.P

respectively .Same number should be multiplied in Rs. also

Q R

C.P 7×11 9× 11=99

S.P 11× 7 13× 7=91

P/L=S.P=C.P 99-77=22 L%=8

99× 100

=8.08%

Exp 9: Nahid bought some oranges 11 for Rs.9 and same number 9 for Rs. 11 and sold them at 1 for Rs. 2.Find

Profit /Loss %

Q R Total C.P 11×9 9× 𝟗=81 Total Q =198

9×11 11× 𝟏𝟏=121 Total C.P=81+121=202

S.P 2× 𝟏𝟗𝟖=396 Profit=396-202=194

P/L P%=194/202=96.03

Exp10:Faraz purchased some lemons .He sold all the lemons ,He sold 8 lemons for Rs. 7 and gained 40 %.In

order to obtain 50 % profit, what should be selling rate?

Solution:

Golden Rule:

𝑪. 𝑷 × 𝑭𝟏 = 𝑭𝟐 × 𝑴. 𝑷 = 𝑺.P

Situation I

S.P of lemon is=7

8

𝐶. 𝑃 × 1.4 =7

8

C.P=7

8×1.4

=10

16

Situation II

10

16× 1.5 = 𝑆. 𝑃

15

16 =S.P

So he must sell 16 for Rs. 15

Q R

C.P 7 9

S.P 11 13

P/L



Type VI: Table Method for different situation

Exp11: Haq bought a chair and sold it at a gain of 10 % .If he had bought it at 20 %

less and sold it for 10 more; he would have gained 40 %.Find the C.P?

Solution: Let C.P=100x

I II 30x+10=40% of 80x

30x+10=32x

x=5

C.P=100× 𝟓

=500

C.P 100x 80x

S.P 110x 110x+10

P?L 10x S.P-C.P=110x+10-80x

=30x+10

Exp 12: If an article is sold for Rs. 178 at a loss of 11%, what should be its S.P in order to earn a profit of 11

%?

Solution: C.P=100x

I II

C.P 100x 100× 𝟐=200 200

S.P 178=100x-11x=89x, x=2 200× 𝟏. 𝟏𝟏=222

P/L 11x 10%

Exp 13: An article is sold at a profit of 20% If it had been sold at a profit of 25 % it would have fetched Rs. 35

more .Find C.P?

Solution: Let C.P=100x

I II

C.P 100x 100x C.P=100x=100× 𝟕=700

S.P 120x 125x

P/L 20x 25x 25x-20x=35,x=7

Type VI When C.P of x articles=S.P of Y articles

Finds S.P/C.P=F(Factor)

Calculate profit according to factor

Exp14: If the cost price of 50 oranges is equal to the selling price of 40 oranges, Find P%

Solution: Given that

50C.P=40S.P

S.P/C.P=1.25

So profit will be 25%



Exp 15: By selling 75 mt of cloth, Saddam gain the selling price of 25 mt. Find

gain %?

Solution:

Profit=S.P-C.P

25S.P=75S.P-75C.P

50S.P=75C.P

S.P/C.P=1.5=F1

So there will be 50 % profit.

Type VII: Dishonest Dealer

Profit %=𝐸𝑟𝑟𝑜𝑟 𝑉𝑎𝑙𝑢𝑒

(𝑇𝑟𝑢𝑒 𝑉𝑎𝑙𝑢𝑒 −𝐸𝑟𝑟𝑜𝑟 𝑉𝑎𝑙𝑢𝑒× 100

If a corrupted shopkeeper makes x% while purchasing an item and y% while selling an item, then his profit % will

be

Profit %= 𝑥 + 𝑦 +𝑥𝑦

100

Exp16: A dishonest fruit vendor professes to sell his goods at cost price but he uses a weight of 800 gm for the

Kg weight. Find the gain %?

Solution: Profit %=𝐸𝑟𝑟𝑜𝑟 𝑉𝑎𝑙𝑢𝑒

(𝑇𝑟𝑢𝑒 𝑉𝑎𝑙𝑢𝑒 −𝐸𝑟𝑟𝑜𝑟 𝑉𝑎𝑙𝑢𝑒× 100

Profit %=200

(1000−200× 100

=25%

Concept:

Let 1 gm =1 Rs.

He pretended 1000gm. =1000 Rs. (S.P)

But he actually gave 800 gm. =800 Rs. (C.P)

S.P/C.P=1000/800=1.25=F1

So there will be a profit of 25%.



• A dishonest shopkeeper sells an item for 10% profit but he makes a foul by

giving that item 20% less by weight. So the profit % he makes will be

Direct formula: Profit %=𝟏𝟎𝟎(𝐩𝐫𝐨𝐟𝐢𝐭 % + % 𝐥𝐞𝐬𝐬 𝐛𝐲 𝐰𝐞𝐢𝐠𝐡𝐭)

(𝟏𝟎𝟎−% 𝐥𝐞𝐬𝐬 𝐛𝐲 𝐰𝐞𝐢𝐠𝐡𝐭)

Exp17: A dishonest fruit vendor professes to sell his goods at a profit of 10%, but he uses a weight of 16 gm for

20 gm. Find his gain%?

Solution: Let 1 gm=1 Rs.

He pretended to give 20 gm=20 Rs.

And take 10 % profit on Rs. 20=20+10% of 20=20+2=22(S.P)

But he actually gave 16gm. =16Rs. (C.P)

S.P/C.P=22/16=1.375 F1

So there be will 37.5% profit

Type IX: Common Loss /Gain

Same C.P: No profit No loss

Same S.P: always loss L% =(𝐶𝑜𝑚𝑚𝑜𝑛 𝐿𝑜𝑠𝑠/𝐺𝑎𝑖𝑛 )2

100

A man sells two items at the same price P and he make a profit of x on first item and a loss of y on second item, then

Profit/loss %=(100(x−y)−2xy )

(200+x−y)



Exp18: Fareed sold two types of goods for Rs. 100000 each. On one of them, he lost

20 % and on the other he gained 20%.His gain or loss %?

Solution: Same S.P:

L% =(20)2

100

=4 %( loss)

If we want to calculate in Rs.

Let C.P for both article is =100x

Loss=4x

S.P=96x=2× 1𝑙𝑎𝑐

X=2

96

Loss=4x=4×2

96=

1

12lacs

Exp 19: A trader bought two horses for Rs 19500.He sold one at a loss of 20 % and the other at a profit of 15

%. If the selling price of each horse is same, then their C.P is:

Solution:

Take 80x+115x=19500

X=100

So price will be 11500 and 8000

Mix

A man losses x% when he sells an item for z. if he wants to make a profit of y%, then

SP= ( 100+y z)

(100−𝑥)

A person sells an item for x% profit. If he sells it for z money more, he would make a profit of y%, then

CP=100×z

(𝑦−𝑥)

·

profit and loss

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