*Profit and Loss***Important Facts:**

**Cost Price**: The price at which an article is purchased,

is called its cost price,abbreviated as C.P.

**Selling Price**: The price at which an article is sold,

is called its selling price,abbreviated as S.P.

**Profit or Gain**: If S.P. Is greater than C.P. The seller

is said to have a profit or gain.

Loss:if S.P. Is less than C.P., the seller is said to

have incurred a loss.

**Formulae**

1.Gain=(S.P-C.P)

2.Loss=(C.P-S.P)

3.Loss or Gain is always reckoned on C.P.

4.Gain%=(gain*100)/C.P

5.Loss%=(loss*100)/C.P

6.S.P=[(100+gain%)/100]*C.P

7.S.P=[(100-loss%)/100]*C.P

8.C.P=(100*S.P)/(100+gain%)

9.C.P=(100*S.P)/(100-loss%)

10.If an article is sold at a gain of say,35%,then S.P=135% of C.P.

11.If an article is sold at a loss of say,35%,then S.P=65% of C.P.

12.When a person sells two similar items, one at a gain of say,

x%,and the other at a loss of x%,then the seller always incurs a

loss given by Loss%=[common loss and gain %/10]2=(x/10)2

13.If a trader professes to sell his goods at cost price,but uses

false weight,then Gain%=[(error/(true value-error))*100]%

14.Net selling price=Marked price-Discount

**Simple Problems**

1.A man buys an article for Rs.27.50 and sells it for Rs.28.60

Find the gain percent.

Sol: C.P=Rs 27.50 S.P=Rs 28.60

then Gain=S.P-C.P=28.60-27.50=Rs 1.10

Gain%=(gain*100)/C.P%

=(1.10*100)/27.50%=4%

2.If a radio is purchased for Rs 490 and sold for Rs 465.50

Find the loss%?

Sol: C.P=Rs 490 S.P=Rs 465.50

Loss=C.P-S.P=490-465.50=Rs 24.50

Loss%=(loss*100)/C.P%

=(24.50*100)/490%=5%

3.Find S.P when C.P=Rs 56.25 and Gain=20%

Sol: S.P=[(100+gain%)/100]*C.P

S.P=[(100+20)/100]56.25=Rs 67.50

4.Find S.P when C.P=Rs 80.40,loss=5%

Sol: S.P=[(100-loss%)/100]*C.P

S.P=[(100-5)/100]*80.40=Rs 68.34

5.Find C.P when S.P=Rs 40.60,gain=16%?

Sol: C.P=(100*S.P)/(100+gain%)

C.P=(100*40.60)/(100+16)=Rs 35

6.Find C.P when S.P=Rs 51.70 ,loss=12%?

Sol: C.P=(100*S.P)/(100-loss%)

C.P=(100*51.70)/(100-12)=Rs 58.75

7.A person incurs 5% loss by selling a watch for Rs 1140 . At

what price should the watch be sold to earn 5% profit?

Sol: Let the new S.P be Rs x then,

(100-loss%):(1st S.P)=(100+gain%):(2nd S.P)

(100-5)/1140=(100+5)/x

x=(105*1140)/95=Rs 1260

8.If the cost price is 96% of the selling price,then what is

the profit percent?

Sol: let S.P=Rs 100 then C.P=Rs 96

profit=S.P-C.P=100-96=Rs 4

profit%=(profit*C.P)/100%

=(4*96)/100=4.17%

9.A discount dealer professes to sell his goods at cost price

but uses a weight of 960 gms for a Kg weight .Find his gain %?

Sol: Gain%=[(error*100)/(true value-error)]%

=[(40*100)/1000-40)]%=25/6%

10.A man sold two flats for Rs 675,958 each .On one he gains

16% while on the other he losses 16%.How much does he gain or

lose in the whole transaction?

Sol: loss%=[common loss or gain%/10]2=(16/10)2=2.56%

11.A man sold two cows at Rs 1995 each. On one he lost 10% and

on the other he gained 10%.what his gain or loss percent?

Sol: If loss% and gain% is equal to 10

then there is no loss or no gain.

12.The price of an article is reduced by 25% in order to

restore the must be increased by ?

Sol: [x/(100-x)]*100 =[25/(100-25)]*100

=(25/75)*100=100/3%

13.Two discounts of 40% and 20% equal to a single discount of?

Sol: {[(100-40)/100]*[(100-20)/100]}%=(60*80)/(100*100)%

=48%

single discount is equal to (100-48)%=52%

**Difficult Problems**

1.The cost of an article including the sales tax is Rs 616.The

rate of sales tax is 10%,if the shopkeeper has made a profit

of 12%,then the cost price of the article is?

Sol: 110% of S.P=616

S.P=(616*100)/110=Rs 560

C.P=(100*S.P)/(100+gain%)

C.P. =(100*560)/(100+12)=Rs 500

2.Sam purchased 20 dozens of toys at the rate of 375 Rs per dozen.

He sold each one of then at the rate of Rs 33.What was his

percentage profit?

Sol: C.P of one toy=Rs 375/12=Rs 31.25

S.P of one toy=Rs 33

profit=S.P-C.P=33-31.25=Rs 1.75

profit %=(profit/C.P)*100

=(1.75/31.25)*100

profit% =5.6%

3.Two third of consignment was sold at a profit of 5% and the

remainder at a loss of 2%.If the total was Rs 400,the value of the

consignment was?

Sol: let the total value be Rs x

value of 2/3=2x/3, value of 1/3=x/3

total S.P value be Rs x

total S.P=[(105% of 2x/3)+(98% of x/3)]

=(105*2x)/(100*3)+(98/100)+x/3

=308x/300

(308x/300)-x=400

8x/300=400

x=(300*400)/8=Rs 15000

4.Kunal bought a suitcase with 15% discount on the labelled price.

He sold the suitcase for Rs 2880 with 20% profit on the labelled

price .At what price did he buy the suitcase?

Sol: let the labelled price be Rs x

then 120% of x=2880

x=(2880*100)/120=Rs 2400

C.P=85% of the 2400

(85*2400)/100=Rs 2040

5.A tradesman gives 4% discount on the marked price and gives

article free for buying every 15 articles and thus gains 35%. The

marked price is above the cost price by

Sol: let the C.P of each article be Rs 100

then C.P of 16 articles=Rs (100*16)=Rs 1600

S.P of 15 articles =1600*(135/100)=Rs 2160

S.P of each article =2160/15=Rs 144

If S.P is Rs 96, marked price =Rs 100

If S.P is Rs 144,marked price =(100/96)*144=Rs 15000

therefore marked price=50% above C.P

6.By selling 33m of cloth ,one gains the selling price of 11m.Find

the gain percent?

Sol: gain=S.P of 33m-C.P of 33m

=11m of S.P

S.P of 22m=C.P of 33m

let C.P of each meter be Rs 1,then C.P of 22m=Rs 22

S.P of 22m=Rs 33

gain=S.P-C.P=33-22=Rs 11

gain%=(gain/C.P)*100

=(11/22)*100=50%

7.The price of a jewel, passing through three hands, rises on the

whole by 65%.if the first and second sellers earned 20% and 25%

profit respectively,find the percentage profit earned by the

third seller?

Sol: let the original price of the jewel be Rs P and

let the profit earned by the third seller be x%

then (100+x)% of 125% of P=165% of P

[(100+x)/100]*(125/100)*(120/100)*P=(165/100)*P

100+x=(165*100*100)/(125*120)

100+x=110

x=10%

8.When a producer allows 36% commission on the retail price of his

product ,he earns a profit of 8.8%.what would be his profit

percent if the commission is reduced by 24%

Sol: let retail price =Rs 100

commission=Rs 36

S.P=retail price-commission=100-36=Rs 64

But profit=8.8%

C.P=(100*C.P)/(gain+100)=(100*64)/(100+8.8)=Rs 1000/17

new commission=Rs 12

new S.P=100-12=Rs 88

gain=88-(1000/17)=Rs 496/17

gain%=gain*100/C.P

=(496*17*100)(17*1000)

gain%=49.6%

9.Vikas bought paper sheets for Rs 7200 and spent Rs 200 on

transport. Paying Rs 600,he had 330 boxes made,which he sold

at Rs 28 each. His profit percentage is

Sol: total investments=7200+200+600=Rs 8000

total receipt=330*28=Rs 9240

gain=S.P-C.P

=total receipt-total investments

gain=9240-8000=Rs 1240

gain% =gain*100/C.P=1240*100/8000=15.5%

10.A person earns 15% on investment but loses 10% on another

investment .If the ratio of the two investments be 3:5 ,what is the

gain or loss on the two investments taken together?

Sol: let the investments be 3x and 5x

then total investment=8x

total receipt=115% of 3x+90% of 5x

=115*3x/100+90*5x/100=7.95x

loss=C.P-S.P=8x-7.95x=0.05x

loss%=.05x*100/8x=0.625%

11.The profit earned by selling an article for Rs 900 is double the

loss incurred when the same article is sold for Rs 490 .At what

price should the article be sold to make 25% profit?

Sol: let C.P be Rs x

900-x=2(x-450)

3x=1800

x=Rs 600

C.P=Rs 600 , gain required=25%

S.P=(100+gain%)*C.P/100

S.P=(100+25)*600/100=Rs 750

12.If an article is sold at 5% gain instead of 5% loss,the seller

gets Rs 6.72 more. The C.P of the article is?

Sol: let C.P be Rs x

105% of x-95% of x=6.72

(105/100)*x-(95/100)*x=6.72

x/10=6.72

x=Rs 67.21.

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