PROFIT AND LOSS

This is applicable to our daily life too. So studying this portion not only helps in acheiving high rank in various exams but also helps in gaining better life.

TYPE - I

Gain = Selling Price (SP) - Cost Price (CP)
Loss = CP - SP
Gain%=Gain*100/CP
Loss% =Loss x 100/CP

EXAMPLES

1.

Arun bought chocolates for Rs. 500 and sold it for Rs. 650. Find his gain percent.
CP =500; SP =650
Profit = 650 - 500 = Rs. 150
Gain% = 150/500*100=30%

2.

If the loss % of an article is 20 and the cost price is Rs. 5050, find the selling price of the article.
Loss%=Loss*100/CP
20 = Loss x 100
CPLossx100/5050
Loss=505*2=1010
SP=CP-loss
=5050-1010=4040
.'. Selling price of the article = RS.4040

3.

Binoj buys a cycle for Rs. 4700 and
spends Rs. 800 on its repairs. If he sells
the cycle for Rs. 5800, find his gain percent.
CP = 4700  800 = Rs. 5500 
SP = Rs.5800
Gain = Rs.(5800 - 5500) = Rs. 300
Gain%=[Gain* 100/CP]
[300x100/5500]=5 5/11%
.'.Gain% =5 5/11

4.

If the selling price is doubled, the profit triples. Find the gain percent.
Let CP be Rs. x and SP be Rs.y 
Then, 3(y - x) = (2y - x)
=> y = 2x
Gain = Rs. (y - x) = Rs. (2x - x) = Rs, x
.'.Gain% =[x/x * 100] = 100%
.'.Gain% = 100

TYPE-II

*Loss or gain is always reckoned on CP
*SP=[100Gain%/100]*CP
*SP = [100Loss%/100] xCP

EXAMPLES

1.

Sajan bought a car for Rs:80000 and sells it at a loss of 10%. What is the selling price of the car
CP = Rs. 80,000 Loss % = 10
SP = (100-Loss% / 100)*CP
(100-10/100)*80000
=90/100x 80,000 = 72,000
.'.Selling Price of the car is Rs. 72,000

2.

The cost price of 30 articles is the same as the selling price of x articles. If the profit is 20%, then the value of x is__ 
Let CP of each article be Re.1 
.'.CP of x articles = Rs. x 
SP of x articles = Rs. 30
Profit = Rs. (30 - x)
.'.[30-x/x*100]=20
100 (30-x) = 20x 
3000-100X = 20x 
120x = 3000 
x=3000/120
.'.x=25

3.

The percentage profit earned by selling an article for Rs. 2500 is equal to t percentage loss incurred by selling the same article for Rs. 2200. At what price should the article be sold to make 50% profit.
Let CP be Rs. x
Then, 2500 -x /x *100 =x-2200/x*100
=>2500 - x = x - 2200
2x = 4700 
x = 2350
.'.Required SP = 150% of CP
=150/100*2350=3525
.'.Required SP = Rs. 3525

4.

Amir bought a bag full of articles at the rate of 7 for Rs. 9 and sold all of them at the rate of 8 for Rs. 11. If he gained Rs. 10, how many articles did they bag contain
No. of articles bought = LCM of 7 and 8 = 56
CP of 56 pencils =9/7*56 = Rs. 72
SP of 56 pencils =11/8*56 = RS. 77
Now, Rs. 5 are gained on 56 pencils
So Rs. 10 are gained on 56/5xl0=l 12 
.'. No. of articles = 112

5.

Kishor sold 2 bikes for Rs. 75,000 each. On one he gains 10% and on the other, he loses 10%. Find his gain or loss % in this whole transaction.
In such cases, loss is incurred always.
Loss%( common loss or gain percent/10)^2%
=(10/10)^2=1%
.'.LOSS % = 1

6.

Profit earned by selling an article for Rs. 700 is same as the loss incurred by selling the article for 620. What is the cost price of the article.
Let CP =x
.'.700-x = x-620
2x =1320
x=660
.'.Cost price of the article is Rs. 660

7.

If a shopkeeper reduced the selling price of cookware from Rs. 700 to Rs. 680, his loss increases by 2%. Find the cost price of the cookware 
Let CP be x
Then, 2% of x = (700-680) =20
2x/100=20
x = 1000
.'.cost price = Rs.1000

TYPE - III

*If discount offered is 30%, then final price you have to pay is (100 - 30)% of
the original price = 70/100 = 0.7 times original price.
*If successive discount 15% (two times) is offered, final price you have to pay is 0.85 x 0.85 x original price = 0.7225 x original price.
*Discount is given on marked price.
*Profit or loss is always calculated on cost price (actual investment)

EXAMPLES

1.

Sanju marked the price tags of all his mobile phones, 10% above the cost
price. And then he offers 10% discount on their marked price. What is his profit or loss%
Let the cost price be Rs.100 
Marked price = 10% above cost price 
ie, Marked price =110% of cost price
=110/100*100
= Rs. 110
10% discount on Marked Price => 0.9 times 
=0.9*110=Rs.99
.'.Selling Price = Rs. 99
Loss = 100 - 99 = 1%

2.

A bracelet carrying a sale price ticket of Rs. 25,000 is sold at a discount of 5%, there by gaining 20%. The cost price of the bracelet is____ 
Given,Marked Price = Rs. 25,000
Discount = 5%
SP=25000x95/100
Gain = 20%
.'.CP = 100/120*SP 
= 100/120 x25000x95/100
= 19791.67 
=19792
.'.cost price of the bracelet = Rs. 19792

3.

An induction cooker is listed at Rs. 2700 and 2 successive discounts of 3% and 3% are given on it. How much would the seller gain or loss, if he gives a single discount of 6% instead of two discounts
1st Case
SP = 97% of 97% of 2700
=97/100*97/100*2700
=2540.43
2nd Case 
SP = 97% of 2700
94/100*2700=2538
Loss = 2540.43-2538=2.43
.'.Loss = Rs.2.43

4.

The SP of an ironbox after two successive discounts of 20% and 10% on marked price is Rs. 3480. Find the marked price.
Let the marked price be x.
Given,x* 80/100*90/100=3480 
.'.3480*100*100/80*90
=34800000/7200=4833.33
.'. Marked price = Rs.4833.33