11. PROFIT AND LOSS
IMPORTANT FACTS
COST PRICE: THE PRICE AT
WHICH ARTICLE IS PURCHASED.ABBREVATED AS C.P.
SELLING PRICE: THE PRICE AT WHICH ARTICLE IS SOLD.
PROFIT OR GAIN:IF SP IS GREATER THAN CP,THE SELLING PRICE IS SAID TO HAVE
PROFIT OR GAIN.
LOSS: IF SPIS LESS THAN CP,THE SELLER IS SAID TO INCURED A LOSS.
FORMULA
1.GAIN=(SP)-(CP).
2.LOSS=(CP)-(SP).
3.LOSS OR GAIN IS ALWAYS RECKONED ON CP
4. GAIN %={GAIN*100}/CP.
5.LOSS%={LOSS*100}/CP.
6.SP={(100+GAIN%) /100}*CP.
7.SP={(100-LOSS%)/100}*CP.
8.{100/(100+GAIN%)} *SP
9.CP=100/(100-LOSS%)}*SP
10.IF THE ARTICLE IS SOLD AT A GAIN OF SAY 35%, THEN SP =135% OF CP
11.IF A ARTICLE IS SOLD AT A LOSS OF SAY 35%.
THEN SP=65% OF CP.
12.WHEN A PERSON SELLS TWO ITEMS,ONE AT A
GAIN OF X% AND OTHER AT A LOSS OF X%.THEN THE SELLER ALWAYS INCURES A LOSS
GIVEN:
{LOSS%=(COMON LOSS AND GAIN ) 2}/10.=(X/10) 2
13.IF THE TRADER PROFESSES TO SELL HIS GOODS
AT CP BUT USES FALSE WEIGHTS,THEN
GAIN=[ERROR/(TRUE VALUE)-(ERROR)*100]%
SOLVED PROBLEMS
ex.1 A man buys
an article for rs.27.50 and sells it for rs.28.50. find his gain %.
sol. cp=rs27.50, sp=rs 28.50
gain=rs(28.50 –27.50)=rs1.10
so gain%={(1.10/27.50)*100}=4%
Ex.2. If the a radio is sold for rs 490 and sold for
rs 465.50.find loss%.
sol. cp=rs490,sp= 465.50.
loss=rs(490-465.50)=rs 24.50.
loss%=[(24.50/490)*100]%=5%
Ex.3.find S.P when
(i)CP=56.25,gain=20%.
sol.
(i)SP =20% of rs 56.25
,=rs{(120/100)*56.25}=rs67.50.
(ii)CP=rs 80.40,loss=5%
sol: sp=85% of rs 80.40
=rs {(85/100)*80.40}=rs 68.34.
ex.4 find cp
when:
(i)
sp =rs 40.60 : gain=16%
(ii)
sp=rs51.70:loss=12%
(i)
cp=rs{(100/116)*40.60}=rs
35.
(ii)
cp=rs{(100/88)*51.87}=rs58.75.
ex.5 A person incures loss for by
selling a watch for rs1140.at what price should the watch be sold to earn
a 5% profit ?
sol. let the new sp be rsx.then
(100-loss%) : (1st
sp)=(100+gain%) (2nd
sp)
ð
{(100-5)/1400}={(100+5)/x}=>
x={(105*1140)/95} =1260.
ð
ex.6 A book was sold for rs 27.50 with a profit of
10%. if it were sold for rs25.75, then what would be % of profit or loss?
sol.
SP=rs 27.50: profit =10%.
sol. CP=rs {(100/110)*27.50}=rs 25.
When sp =Rs25.75 ,profit =Rs(25.75-25)=Rs 0.75
Profit%={(0.75/25)*100}%=25/6%=3%
Ex7 .If the cost price is 96% of sp then whqt is the
profit %
Sol. sp=Rs100 :
then cp=Rs 96:profit =Rs 4.
Profit={(4/96)*100}%=4.17%
Ex.8. The cp of 21 articles is equal to
sp of 18 articles.find gain or loss %
CP of each article
be Rs 1
CP of 18 articles
=Rs18 ,sp of 18 articles =Rs 21.
Gain%=[(3/18)*100]%=50/3%
Ex.9 By selling 33 metres of cloth , one gains the
selling price of 11 metres . Find the gain percent .
Sol:
(SP of 33m)-(CP of 33m)=Gain=SP of 11m
SP of 22m = CP of 33m
Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33.
Gain%=[(11/22)*100]%=50%
Ex10 A vendor bought bananas at 6 for
Rs.10 and sold them at Rs.4 for Rs.6 .Find his gain or loss percent .
Sol:
Suppose , number of bananas bought = LCM of 6 and 4=12
CP=Rs.[(10/6)*12]=Rs.20 ; SP=
Rs[(6/4)*12]=Rs.18
Loss%=[(2/20)*100]%=10%
Ex.11. A man
brought toffees at for a rupee. How many for a rupee must he sell to gain 50%?
Sol. C.P
of 3 toffees=Re 1; S.P of 3 toffees =150% of Re.1=3/2.
For Rs.3/2, toffees sold =3, for Re.1,
toffees sold = [3*(2/3)]
=
2.
Ex. 12.A
grocer purchased 80 kg of sugar at Rs.13.50 per kg and mixed it with 120kg
sugar at Rs.16per kg. At what rate should he sell the mixer to gain 16%?
Sol
.C.P
of 200 kg of mixture = Rs. (80 * 13.50+120*16) = Rs.3000.
S.P =116% 0f Rs.3000 =Rs.[(116/200)
*3000]=Rs.3480.
\ Rate of S.P of
the mixture =Rs.[3480/200] per
kg =Rs.17.40 per kg.
Ex.13. Pure
ghee cost Rs.100 per kg. After adulterating it with vegetable oil costing Rs.50
per kg, A shopkeeper sells the mixture
at the rate of Rs.96 per kg, thereby making a profit of 20%.In What ratio does
he mix the two?
Sol. Mean
cost price =Rs. [ (100/120)*96 ]
=Rs.80 per kg.
By the rate of allegation :
C.P of 1kg ghee
C.P of 1kg oil
100
50
Mean price
80
 |
 |
30
20
\ Required ratio
=30:20 =3:2.
Ex. 14.
A dishonest dealer professes to sell his goods at cost price but uses a
weight of 960 gms for a kg weight . Find his gain percent.
Sol
.Gain%
=[ Error *100 ]% = [(40/960)*100] % =
4 1 %
(error value)-(error)
6
Ex 15. If the manufacturer
gains 10%,the wholesale dealer 15% and the retailer 25% ,then find the cost of production of a
,the retail price of which is Rs.1265?
Sol:
Let the cost of production of the table be Rs
x
The ,125% of 115% of 110% of x=1265
ð 125/100*115/100*110/100*x=1265=>253/160*x=>1265=>x=(1265*160/253)=Rs.800
Ex16
. Monika purchesed a pressure cooker at 9/10th of its selling price
and sold it at 8% more than its S.P .find her gain percent.
Sol:
Let the s.p be Rs. X .then C.P =
Rs.9x/10,Receipt=108% of rs.x=Rs 27x/25
Gain=Rs
(27x/25*9x/10)=Rs(108x-90x/100)=Rs18x/100
Gain%=(18x/100*10/9x*100)%=20%
Ex .17 An article is sold at certain
price. By selling it at 2/3 of its price one losses 10%,find the gain at
original price ?
sol:
let the original s.p be Rs x. then now
S.P=Rs2x/3,loss=10%
now C.P=Rs20x/27*27/20x*100)%=35%
Ex .18. A tradesman sold an article at a loss of 20%.if the selling
price has been increased by Rs100,ther would have been a gain of 5%.what was
the cost price of the article?
Sol:
Let C.P be Rs x. then (105% of x)-(80 % of
x)=100 or 25% of x=100
ð x/4=100 or x=400
ð so,C.P =Rs 400
Ex 19. A man sells
an article at a profit of 25%if he had bought it 20% less and sold it for Rs 10.50 less,he would have gained 30%find
the cost price of the article.
Sol:
Let the C.P be Rs x
1st S.P=125% of x
=125x/100=5x/4;2nd S.P=80% of x=80x/100=4x/5
2nd S.P=130% of
4x/5=(130/100*4x/5)=26x/25
=>5x/4-26x/25=10.50óx=(10.50*100)/21=50
hence C.P=Rs.50
Ex 20.The price of the jewel,passing through three hands,rises on
the whole by65%.if the first and the second sellers 20%and25% profit
respectively find the percentage profit earned by the third seller.
Sol:
Let the orginal price of the jewel be
Rs p and let the profit earned by the
thrid seller be x%
Then,(100+x)%
of 125% OF 120% OF P=165% OF P
ð
((100+X)/100*125/100*120/100*P)=(165/100*P)
ð
(100+X)=(165*100*100)/(125*120)=110=>X=10%
Ex21 . A man 2 flats for Rs 675958 each.on one he
gains 16% while on the other he losses 16%. How much does he gain/loss in the
whole transaction?
Sol:
In this case there will be alwalys loss.
The selling price is immaterial
Hence, loss % = (common loss and gain%)2
/10=(16/10)%=(64/25)%=2.56%
Ex.22.
A dealer sold three-fourth of his article at a gain of 20% and remaining at a
cost price. Find the gain earned by him at the two transcation.
Sol:
Let the C.P of the whole be Rs x
C.P of 3/4th =Rs 3x/4,C.P of 1/4th
=Rs x/4
ð
total S.P=Rs [(120%of
3x/4)+x/4]=Rs(9x/10+x/4)=Rs 23x/20
ð
gain=Rs(23x/20-x)=Rs 3x/20
ð
gain%=3x/20*1/x*100)%=15%
Ex
23 ..A man bought a horse and a car riage for Rs 3000.he sold the horse at a
gain of 20% and the carriage at a loss of 10%,thereby gaining 2% on the
whole.find the cost of the horse.
Sol:
Let the C.p of the horse be Rs.x, then C.P
of the carriage =Rs(3000-x)
20%
of x-10% of(3000-x)=2% of 3000
ð
x/5-(3000-x)/10=60=.2x-3000+x=600=.3x+3600=>x=1200
ð
hence,C.P of the horse =Rs 1200
Ex
24 find the single discount equivalent
to a series discount of 20% ,10% and 5%’
sol:
let the marked price be Rs 100
then
,net S.P=95% of 90% of 80% of Rs 100
=Rs(95/100*90/100*80/100*100)=Rs68.40
Ex
.25 After getting 2 successive discounts, a shirt with a list price of Rs 150
is available at Rs 105. If the second discount is 12.55,find the first
discount.
Sol:
Let the first discount be x%
Then,87.5% of (100-x)% of 150= 105
ð
87.5/100*(100-x)/100*450=150=>105=>100-x=(105*100*100)/(150*87.5)=80
ð
x=(100-80)=20
ð
first discount = 20%
Ex
.26 An uneducated retailar marks all its goods at 50% above the cost price and
thinking that he will still make 25% profit,offers a discount of 25% on the
marked price.what is the actual profit on the sales?
Sol:
Let C.P =Rs 100.then ,marked price =Rs100
S.P=75%
of Rs 150=Rs112.50
Hence,gain%=12.50%
Ex27
.A retailer buys 40 pens at the market price of 36 pens from a wholesaler ,if
he sells these pens giving a discount of 1% ,what is the profit % ?
sol:
let the market price of each pen be Rs 1
then,C.P of 40 pens = Rs 36 S.P of 40 pens
=99% of Rs 40=Rs 39.60
profit
%=((3.60*100)/36) %=10%
Ex
28 . At what % above C.P must an article be marked so as to gain 33% after
allowing a customer a discount of 5%?
Sol
Let C.P be Rs 100.then S.P be Rs 133
Let the market price be Rs x
Then 90% of
x=133=>95x/100=133=>x=(133*100/95)=140
Market
price = 40% above C.P
Ex
.29 . When a producer allows 36% commission on retail price of his product, he
earns a profit of 8.8%. what would be his profit % if the commision is reduced
by 24%?
Sol:
Let the retail price =Rs 100.then,
commission=Rs 36
S.P=Rs(100-36)=Rs 64
But,
profit=8.8%
C.P=Rs(100/108.8*64)=Rs
1000/17
New
commission =Rs12. New S.P=Rs(100-12)Rs 88
Gain=Rs(88-1000/17)=Rs
496/17
Gain%=(496/17*17/1000*100)%=49.6%
