Arithmetic (profit, loss percentage and simple interest)

            

  Arithmetic:- 

 Profit and Loss Formula - Examples, Derivation, FAQs

Today in this article I will discuss on arithmetic, topics 'Profit Loss and simple interest of class 6' along with percentage also Profit and Loss- Formula,Definition,Calculation, Examples.Hope these will help on going school students a lot.     

Profit loss percentage questions.

What is profit?

Answer:—

• When selling price of an article is more than its cost price or buying price then it is called profit.e.g;if selling price of an article is Rs 25 and its cost price is Rs 20 then we will say there is a profit of  = Rs(25-20) =Rs 5                     

•        i.e; if S.P>C.P, then

•   Profit=S.P—C.P

What is loss?

Answer:-

• When selling price is less than its cost price of an article then we can say that there is loss.Mathematically, if C.P>S.P then loss occurs.

• Loss:-C.P-S.P

Some

Profit and loss examples with answer.

• 1. A shop keeper bought one dozen bananas with Rs 60 and sold them with Rs 80,find his profit or loss.

Answer:-

• Here, Cost price of bananas=Rs 60 

• Selling price of bananas=Rs 80

•    Selling price>Cost price

•      Profit=Rs(80-60)            

•  =Rs 20

2.A person bought a hand watch with $50 and sold it with a price of $40 find his profit or loss.

Answer:-

• Here,   

• Cost price of watch=$50 

•   Selling price of watch=$40

•   Cost price>selling price

•    Loss =   $(50-40)

•             =   $10

3.A shop keeper bought 100 eggs with $100 and later he sold 60 eggs @ $2 and remaining @ $4 find his overall profit or loss.

Answer:-

• 1st case,

•  The selling price of 1egg= $2

•  The selling price of 60 eggs =$(2×60)

•                                                 =$120 

•  2ndcase:-

•  The selling price of 1 egg=$4

•  The selling price of40 eggs =$(4×40)

•                                               =$160

•  Total selling price of100 eggs=$(120+160)

•                                                 =$280

•  Again cost price of100 eggs=$100

• Here,

•   selling price>cost price

So,

•    Profit=$(280-100)          
•             =$180

Profit and loss percentage formula

can be described as follows:-

• Selling price =(100+profit%)/100×C.P

• Selling price =(100-loss%)/100×C.P

      
 C.P= Cost price.

 Where,

• Cost price =(100/100+profit%)×S.P
• Cost price =(100/100-loss%)×S.P

Where,

S.P = Selling price.

• Profit%= {(Profit/C.P)×100}%
• Loss%= {(Loss/C.P)×100}%

Problem:-

Selling an article on Rs250 a person gains Selling an article on Rs250 a person gains 15% profit find the cost price of the article.

Answer:-

Here,

• S.P=Rs250
• Profit=15%
• C.P=?
• C.P = (100/100+profit%)×S.P
• = Rs(100/100+15)×250
• = Rs(100/115)×250
• = Rs(20/23)×250
• = Rs 5000/23
• = Rs 217.39

Costprice:-

• The amount paid to purchase an article or the price at which an article is made is known as its cost price.The cost price is abbreviated as C.P.

SellingPrice:-

• The price at which an article is sold is known as its selling price.The selling price is abbreviated as S.P

What is percentage?

Solution:-

• In,mathematics percentage is a number or ratio which is determined as a fraction of 100.

       e.g; 20%=20/100

• when we compare two same quantities with respect to100 then the word percent comes.

● If 30% of X is 240,then find X.

Answer:-

     

• 30 % of X = 240

• => (X×30)÷100=240

• =>30X÷100=240

• =>30X=240×100

• =>X=24000÷30

• =>X=800

  Required,
   X=800
● Mr.Jhon started a job with salary
$20k after 1year later his salary
increased by 25% find his new salary?

Actually,

Answer:-
  

• Starting salary=$20k
•  % of increase of salary=25%
• Amount of increased salary
•   =$(20×25)÷100k

•   =$(500÷100)k

•  =$5k

his new salary will be =  $(20+5)

=$ 25

There are 60 students in a class.If 25% were absent on a particular day,find the number of students present in the class on that day.

• Number of students absent on a particular day = 25% of 60 = 25×60/100                    

•                       =60/4

•                       =15

• Therefore,the number of students present =  60-15  = 45 students.

Solution:-

• Kethrina had $3000 left after spending 40% of the money she took for shopping. How much money did she take along with her?

Solution:

• Let the money she took for shopping=$x
• Money she spent = 40%of x
•                             =40/100 of x
•                             = 4x/10
• Money left with him=(x–4x/10= 6x/10                     
• But money left with her = $3000
• Therefore ,6x/10=3000
• =>x=3000×10/6
• =>x=30000/6
• =>x=5000
•   she took money with her
•         =$5000

Now do yourself:-

• 1.In a class 70% of the students are girls.If the total number of students is 40,what is the number of boys?

• 2.Peter scores 60 marks out of 80 in his mathematics exam.Convert his marks into percent.

• 3.Mason was able to sell 65% of his vegetables before noon.If Mason had 300kg of vegetables in the morning,how many grams of vegetables was he able to sell by noon?

• 4.Alexander was able to cover 55% of 150 km journey in the morning.What percent of journey is still left to be covered?

• 5.A cow gives 40 litre milk each day.If the milkman sells 75% of the milk,how many liters of milk is left with him.

What is simple interest?

Answer:-


Illustration:-

An interest which is calculated only principal amount at a some fixed rate for a definite period of time is known as simple interest.

Suppose,we have borrowed a sum of $100 from MrJohn on a condition that we will return the money after one month and MrJhon also urged us you must give an extra sum of $10 with$100 when returned this extra sum of money $10 is simple interest for a period of one month and rate of interest@$10 as it is calculated on $100.

Formula which is used to find simple interest is given by,

• S.I=P×N×R/100
  
• Where,
• P=Principal or Initial borrowed amount.
• N=Number of years for
• which S.I will be calculated
• R=Rate of interest on
• which S.I will be calculated.

● Amount(A)=P+S.I

  

 Where,
A=Amount
       S.I=Simple interest
 

P=S.I×100/R×N
   

 Where,

    R=Rate of S.I
    N=Number of years.

● R=S.I×100/P×N
  where,
R=Rate of S.I
N=Number of years
P=Principal

● N=S.I×100/P×R
where,
N=Number of years
P=Principal
R=Rate of S.I
S.I=Simple interest.

Problems:-

● If principal=$500 rate of interest @2% per annum for 3years then,find simple interest for that period of time.

Solution:-

• Principal(P)=$500
• Rate of interest(R%)
•    =2%
•   =>R/100=2/100
•    R=2
• Time(N)=3years
•  S.I=P×N×R/100
•      =$500×3×2/100
•      =$5×3×2
•      =$30

Required S.I=$30

• Mr Das borrowed Rs1000
• from Punjab National Bank
• after 2years later he paid S.I
• Rs500,how much rate of S.I
• he had to pay?

Solution:-

• Principal(P)=Rs1000
• Time(N)=2years
• S.I=500
•  R=?
• Let,
• The rate of interest=R%
•     R=S.I×100/P×N
•       =Rs500×100/1000×2
•       =Rs50000/2000
•       =Rs 50/2
•       =Rs 25
• Rate of S.I he paid (R)=25%

   

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FREQUENTLY ASKED QUESTIONS:-

.What is profit formula ?

Answer:- Profit = Selling price - Cost price , Where Selling price> Cost price

What is loss formula ?

Answer:- Loss = Cost price - Selling price, Where cost price>Selling price

What is Percentage profit formula?

Answer :- Profit % = {(profit/cost price) × 100}%

.What is Loss percentage formula ?

Answer:- Loss % = {(Loss/cost price) × 100}%

Gain percentage formula.

Answer :- Gain % = {(Gain/cost price) × 100}%

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