## 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

## 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,

- 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.

### 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,

- 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:-

## 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

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.

### 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?

- 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}%

## .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}%

Very nice.

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