Arithmetic (profit, loss percentage and simple interest)



 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?

    • 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

    What is loss?

    • 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


    Profit and loss examples with answer.

    Profit and Loss Formula - Examples, Derivation, FAQs

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

    • 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.

    • Here,   
    •   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.


    • 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=$100
    • Here,
    •   selling price>cost price
    •    Profit=$(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.


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


    S.P = Selling price.

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


    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.


    • 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


    • 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.


    What is percentage?


    • 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.


    • 30 % of X = 240
    • => (X×30)÷100=240
    • =>30X÷100=240
    • =>30X=240×100
    • =>X=24000÷30
    • =>X=800
    Mr.Jhon started a job with salary
    $20k after 1year later his salary
    increased by 25% find his new salary?



    • 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

    Profit and Loss Formula - Examples, Derivation, FAQs

    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.


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


    • 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?



    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.



           S.I=Simple interest



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

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

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


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


    • 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?


    • 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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    .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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