Profit And Loss, Basic Tricks And Examples

1. Basics Of Profit And Loss

MaNiSH manevandra 01 Jan 1970

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Profit and Loss is a topic that is definitely asked in every placement exam. While the questions are not too tricky, some require deeper understanding of concepts, but most of them are based on certain well-known formulas.

Common terms
o    Profit
o    Loss
o    Cost Price
o    Selling Price
o    Marked Price


Profit(P)
o    The amount gained after selling a product more than its cost price.

Loss(L)
o    The amount, the seller gets after selling the product less than its cost price, is mentioned as a loss.


Cost price
o    The price at which an article is purchased is called its cost price and denoted by cp.
o    For any person, the cost price is an amount or quantity which firstly releases from the pocket of that person.


Selling price
o    The price at which an article is sold is called its selling price, denoted by sp.
o    For any person, the selling price is an amount or quantity which comes to the pocket of that person.

Marked price
o    MRP of an article is known as marked price or labeled price or listed price and denoted by MP
o    Discount always carried on MRP (MP)
o    MRP is always 100 % in the case of a discount.

 Formula

 Profit or gain: if s.p (selling price ) is greater than c.p(cost price) then the seller is said to have a profit or gain i.e

Profit = s.p – c.p

Loss
o    If s.p is less than c.p the seller is said to have a loss. i.e

Loss = c.p – s.p

o    Profit and loss are always counted on c.p
o    C.p is always 100% in the case of profit and loss
o    For any transaction there are two persons involved one is called the buyer and the second one is called seller.




   

2. Profit, Loss And Discount - Examples And Tricks To Solve

MaNiSH manevandra 01 Jan 1970

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In the case of profit or loss, the relation is generated between c.p and s.p 

If 25% profit accrued on an article it means :
100% represents cost price (c.p)
125% represents selling price (s.p)
25% represents profit
i.e. \( 25 \% => 125 \% \ (s.p) \) \( => 100 \% \ (c.p) \)

If 15% loss accrued on an article , it means:
100% represents cost price (cp)
85% represents selling price (sp)
15 % represents loss
i.e \( 15 \% => 100 \% \ (c.p) \) \( => 85 \% \ ( s.p) \)

In the case of discount the relation is generated between sp and mp

If 20% discount accrued on an article its means :
100% represent the marked price (mp)
80% represent the selling price (sp)
20% discount
i.e \( Discount \ 20 \% => 100 \% \ (mp) \) \( =>(100 – 20 \% discount = 80 \% (s.p) \)

Example: A person purchased an article for Rs 120 and sold it for Rs 150 . Find his % profit.
Sol. c.p of the article = Rs 120
s.p of the article = Rs 150
Profit of the person = 150 – 120 = 30
% profit of the person \( = { Profit \over (cp)} \times 100 \)
% profit \(= {30 \over 120} \times 100 \) = 25% (Answer)

Example: A dishonest shopkeeper sells goods at his cost price but uses a weight of 425 gm instead of 500g. Find his gain percent.
Sol. The c.p of shopkeeper = 425gm
The s.p of shopkeeper = 500gm

The profit of shopkeeper = 500 – 425 = 75 gm
% profit of shopkeeper = \( {Profit \ of \ shopkeeper \over c.p \ of \ shopkeeper} \times 100 \) \( = {75 \over 425} \times 100 \)
\( \% Profit = 17 {11 \over 17} \) (Answer)

Example: A person got 5% loss by selling an article for Rs 1045 . At what price should the article be sold to earn 15% profit ?
Sol. Let the new s.p be Rs x then
\({100 – Loss \% \over 1st \ s.p} = {100 + gain \% \over 2nd \ s.p} \) \( = {(100-5) \over 1045}={(100+15) \over x} \)
\( x = {115 \times 1045 \over 95} \) = Rs. 1265 (answer)

[ short trick:] New \( sp = {1045 \over 95} \times 115 = 1265 \)

Example: A person sold an article at profit of 15% if he had sold it at Rs 480 more, he would have gain 18% what is the cost price ?
Sol. Let the c.p of an article be x Rs then ,
=> 115% of x + 480 = 118% of x
=> 118% of x – 115% of c = 480
=> 3 % of x = 480
\( x = {480 \over 3} \times 100 \) = Rs 16000 (answer)

[short trick:]
\( cp = \ {Difference \ in \ sp \over diffrence \ in \ profit \ \%} \times 100 \)
\( cp = {480 \over 3} \times 100 \) = Rs. 16000 (answer)

Example : find the equivalent discount of 10% and 20% .
Sol. Let the MP be = Rs 100
Then net \( sp = 100 \times {90 \over 100} \times {80 \over 100} \) = Rs 72
Required discount = (100 – 72)% = 28% (Answer)

[short trick:]
\( X + Y- {xy \over 100} \)
\( 10+20-{10 \times 20 \over 100} = 28 \% \)

3. Mathematics: Profit And Loss, Solved Questions

MaNiSH manevandra 01 Jan 1970

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Question 1: A person by selling an article at three-fourth of the list price , increase a loss of 20% . Find profit percentage if he sells at the list price.
a) 25%
b) 6.66%
c) 111/9%
d) 20%
e) None of these

Sol. According to question
Let MRP of article \( = x \)
\( \therefore {3 \over 4} x = 80 \)
\( x=80/3*4 \) \( ={320 \over 3}=106{ 2 \over 3} \)
That means Profit % = 6.66%
Answer (b) 6.66%

Question 2: The profit earned by selling an article for Rs 900 is double the loss incurred when the same article is sold for Rs 450. At what price should the article be sold to make a 25% profit?
a)Rs 600
b)Rs 800
c)Rs 750
d)Data inadequate
e)None of these

Sol. Let c.p = Rs x
Then, \( 900 - x = 2 (x – 450) \)
\( 3x = 1800 \)
\( x = 600 \)
Required s.p = 125% of Rs 600 \( = Rs ({125 \over 100} \times 600) \) \( = Rs. 750 \)
Answer : (c) Rs 750

Question 3: A trader who marks his good upto 50% and offered discount of 20% . What % profit the trade makes after offering the payment?
a) 15%
b) 20%
c) 25%
d) 30%
e) 40%

Sol. Let cp = 100,
MRP = 150 \( sp = 150 \times {80 \over 100} \) \( = Rs. 120 \)
Hence, Profit = 20%
Answer: (b) 20%

[short trick:]
By successive formula
\( x+y+{xy \over 100} \)
\( 50-20+{50 \times (-20) \over 100} \)
30 – 10 = 20%