Percentage and profit loss new version 4

this presentation covers the topic percentage, profit and loss aptitude questions in level 1. (basic) categorywise the techniques are supported by suitable examples

1. METHODS
Eight Techniques
1
APPLICATIONS
In Commerce,
Geometry etc.,
2
LINKS
Profit & Loss &
other links
3
PERCENTAGE
SIX PHRASE –VEERARAGAVAN C.S
http://182.72.85.213:8080/AssessmentToolhttp://www.facebook.com/SixPhrase
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PRESENTER NAME SIX PHRASE –The Finishing School 1I

2. SESSION CONTENT
•In this session, we shall learn application of
percentage concept in problems in the areas
of geometry & commerce including profit /
loss.
•Percentage concepts used in other areas such
as alligations/ mixtures are dealt under the
respective session topics.
02-03-2015
VEERARAGAVAN C S, APTITUDE TRAINER,
[email protected]
2

3. X% of a Number
An x % increase
An x% decrease
40% OF 20 MEANS
40
100
??????20=8.
1) If 20% of a = b, then b% of 20 is the same as:
A.4% of aB. 5% of aC.20% of aD. None of these
20% of a = b 
20
100
??????�=�
b% of 20 =
�
100
??????20
b% of 20 =
20
100
??????�??????
1
100
??????20=
4�
100

4. X% of a Number
An x % increase
An x% decrease
Increase by 40% means 140% of that number.
III.Theprice of a product becomes `54 after it increases by 35%.
What was the original price of that product?1)30 2)363)40 4)45
Increase by 35% means 135% of the price is 54.
135
100
??????�????????????�??????��??????�????????????��=54Hence the original price is 54??????
100
135
=40.

5. X% of a Number
An x % increase
An x% decrease
Decrease by 40% means (100–40)60% of that number.
V. The price of a product is reduced to Rs.72 after it is decreased by
10%. What is the original price of the product?1)84 2)90 3)96 4)80
Decreased by 10% means 90% of that price.
Hence the original price is 72??????
100
90
=80.
90
100
??????�????????????�??????��??????�????????????��=72

6. Calculating a percent change
Basically,apercentisasimple
����
�ℎ���
ratio
times100.Whentheyaskyouto
calculatepercentchanges,andhereyou
havetobeverycarefulwithorder,i.e.,
what’sthestartingnumberandwhat’s
theendingnumber.
IMPORTANT:inapercentchange,the
startingnumberisalways100%.Thus,
wecansay:
Percent change =
??????��������ℎ����
�����??????��������
??????100
Hereareacoupleexamples
a)Priceincreasesfrom`400to`500;find
thepercentageincrease.
Ofcourse,that’sachangeof`100,so
`100dividedbystartingvalueof`400is
0.25,times100is25%.Amovefrom`
400to`500isa25%increase.
•b)Pricedecreasesfrom`500to`400;
findthepercentagedecrease.
•Changeisstill`100,butnowthe
startingvalueis`500,and`
100
500
=
0.20,times100is20%.Amovefrom
`500to`400isa20%decrease.
•BIGIDEA:Ordermatters.Whenyou
changefromonevaluetoanother
andwantthepercentagechange,it
matterswhichvaluewasthestarting
value.
02-03-2015
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[email protected]
6

7. PERCENT CHANGE
Thepopulationofatownincreasedfrom1,75,000to2,62,500in
adecade.Theaveragepercentincreaseofpopulationperyear
is:A.4.37%B.5%C.6%D.8.75%
Increasein10years=(262500-175000)=87500.
Herethestartingnumberis175000.
Increase%=
87500
175000
??????100%=50%.
Requiredaverage=
50
10
%=5%.
02-03-2015
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7

8. Percentage
increased by x % then
decreased by y % then
resulting effect in percent
+x –y –
��
100
Increased by x% then again
increased by y% then
+x+y+
��
100
Decreased by x% then
increased by y%
–x+y–
��
100
Decreased by x% then again
decreased by y%
–x –y +
��
100
02-03-2015
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8
If the value of something is
I.Ifthe price of a shirt is increased by 10%
than decreased by 10%. What is the
percent change?
+ 10 -10 –
1010
100
= -1%
The best way to speed up calculations is to
eliminate the need of calculations.

9. 9.RajeevbuysgoodworthRs.6650.Hegetsa
rebateof6%onit.Aftergettingtherebate,he
payssalestax@10%.Findtheamounthewill
havetopayforthegoods.
A. Rs. 6876.10B. Rs. 6999.20
C. Rs. 6654D. Rs. 7000
Total percentage = −6+10−
60
100
=+3.4%
Amount he will pay = 6650∗
103.4
100
=6876.10
02-03-2015
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9

10. PERCENTAGE OF PROFIT & LOSS
100orangesareboughtattherateofRs.350and
soldattherateofRs.48perdozen.
Thepercentageofprofitorlossis:
A.14
2
7
%gainB.15%gainC.14
2
7
%lossD.15%loss
C.Pof100oranges=Rs.350
S.Pof100oranges=
48
12
x100=400.
Profit%=
400−350
350
�100=14
2
7
%gain
02-03-2015
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[email protected]
10

11. Profit percentage
Ifthecostpriceofxarticlesis
equaltothesellingpriceofy
articles,thentheprofitpercentage
isgivenby:�−�
100
�
If Sudhasells 18 articles at the cost
price of 24 articles. Find her profit
percentage?
Here, x= 24 and y= 18
24−18
100
18
=
100
3
=33
1
3
%
02-03-2015 11
Usual Method
Let C.P of 1 article be Rs.x
Then C.P of 24 articles =
24x
S.P of 18 articles = 24x
S.P of 1 article =
24�
18
Profit % =
24??????
18
−�
�
??????100
=24�−18�
100
18
=
100
3
=33
1
3
%

12. QUANTITY
Thecostpriceof20articlesisthesameasthe
sellingpriceofxarticles.
Iftheprofitis25%,thenthevalueofxis:
A.15B.16C.18D.25
Profit%=
x−20
20
�100=25.
X–20=5
X=25.
02-03-2015
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13. TOTAL GAIN / LOSS
A shopkeeper sells one transistor for Rs. 840 at a gain of 20%
and another for Rs. 960 at a loss of 4%.
His total gain or loss percent is:
A. 5
15
17
% lossB. 5
15
17
% gainC. 6
2
3
% gainD.None of these
C.P. of 1st transistor =
100
120
�840= Rs.700
C.P. of 2nd transistor =
100
96
x 960 = Rs.1000
So, total C.P. = Rs. (700 + 1000) = Rs. 1700.
Total S.P. = Rs. (840 + 960) = Rs. 1800.
Gain % =
1800−1700
1700
x 100 = 5
15
17
% gain.
02-03-2015
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13

14. PROFIT IN MIXTURE
Atradermixes26kgofriceatRs.20perkgwith30kg
ofriceofothervarietyatRs.36perkgandsellsthe
mixtureatRs.30perkg.
Hisprofitpercentis:
A.Noprofit,nolossB.5%
C.8%D.10% E.Noneofthese
C.P.of56kgrice=Rs.(26x20+30x36)
=Rs.(520+1080)=Rs.1600.
S.P.of56kgrice=Rs.(56x30)=Rs.1680.
Gain=
1680−1600
1600
�100=5%
02-03-2015
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14

15. SELLING PRICE
A man buys a cycle for Rs. 1400 and sells it at a loss of 15%.
What is the selling price of the cycle?
A. Rs. 1090 B. Rs. 1160
C. Rs. 1190 D. Rs. 1202
S.P =
85
100
??????1400=Rs.1190
02-03-2015
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15

16. SELLING PRICE
ThepercentageprofitearnedbysellinganarticleforRs.1920is
equaltothepercentagelossincurredbysellingthesamearticle
forRs.1280.
Atwhatpriceshouldthearticlebesoldtomake25%profit?
A.Rs.2000 B.Rs.2200
C.Rs.2400 D.Datainadequate
SP
1–CP=CP–SP
2meansCP=
SP
1
+SP
2
2
=
1920+1280
2
=1600.
NewSP=
125
100
x1600=Rs.2000.
02-03-2015
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[email protected]
16

17. Selling Price
BysellingahorseforRs
570atraderloses5%.At
whatpricemusthesellitto
gain5%.
Selling Price(SP)
= given(Rs) X
100±�
100±�??????���%
Selling Price
= 570 X
100+5
100−5
=Rs.630
02-03-2015
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[email protected]
17
USUAL METHOD
S.P = 570 and loss 5%
C.P =
100
100−����
�??????.??????
=
100
95
�570
Profit = 5%
So new S.P
=
100+����??????�
100
????????????.??????
=
105
100
�
100
95
??????570
=Rs.630

18. SELLING PRICE
WhenaplotissoldforRs.18,700,the
ownerloses15%.
Atwhatpricemustthatplotbesoldin
ordertogain15%?
A.Rs.21,000B.Rs.22,500
C.Rs.25,300D.Rs.25,800
S.P=GivenAmtx
100±�����??????��
100±�??????�������������
=18700x
115
85
=Rs.25,300
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Given S.P = 18,700
Loss = 15%
C.P =
100
100−loss
x S.P
=
100
85
X18700
Required = Profit 15%
S.P=
100+����??????�
100
????????????.??????
=
115
100
??????
100
85
??????18700

19. SELLING PRICE
A vendor bought toffees at 6 for a rupee. How
many for a rupee must he sell to gain 20%?
A. 3B. 4C. 5D. 6
C.P of 6 toffees = `.1
S.P of 6 toffees =
120
100
??????1=
120
100
For `
120
100
, no of toffees sold = 6.
For `1, no of toffees sold =
100
120
x 6 = 5.
02-03-2015
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[email protected]
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20. COST PRICE
On selling 17 balls at Rs. 720, there is a loss equal to
the cost price of 5 balls.
The cost price of a ball is:
A. Rs. 45B. Rs. 50
C. Rs. 55D. Rs. 60
(C.P. of 17 balls) -(S.P. of 17 balls) = (C.P. of 5 balls)
C.P. of 12 balls = S.P. of 17 balls = Rs.720.
C.P of 1 ball =
720
12
= Rs.60
02-03-2015
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20

21. PERCENTAGE ERROR
2.Astudentmultipliedanumberby
3
5
insteadof
5
3
.Whatisthe
percentageerrorinthecalculation?
A.34%B.44% C.54% D.64%
Error=correctvalue–wrongvalue=
5
3
−
3
5
=
16
15
Percentageerror=
�����
??????������
??????100=
16
15
5
3
??????100=
16
15
??????
3
5
??????100
64%
02-03-2015
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21

22. PERCENTAGE IN SETS
3.Inacertainschool,20%ofstudentsarebelow8years
ofage.Thenumberofstudentsabove8yearsofageis
ofthenumberofstudentsof8yearsofagewhichis48.
Whatisthetotalnumberofstudentsintheschool?
A.72B.80C.120D.150E.100
Number of students of 8 years of age = 48.
Number of students of 8 years above = 48.
80% of students = 96.
Hence No. of students = 96??????
100
80
=120.
02-03-2015
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23. PERCENTAGE IN SETS
5.In an election between two candidates, one got 55% of the
total valid votes, 20% of the votes were invalid. If the total
number of votes was 7500, the number of valid votes that the
other candidate got, was: A.2700B.2900 C.3000 D.3100
Number of valid votes = 80% of 7500 = 6000.
Valid votes polled by other candidate = 45% of 6000=2700.
02-03-2015
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24. PERCENTAGE IN SETS
6.Threecandidatescontestedanelectionandreceived
1136,7636and11628votesrespectively.
Whatpercentageofthetotalvotesdidthewinning
candidateget?
A. 57%B. 60%C. 65%D. 90%
Total number of votes polled = (1136 + 7636 + 11628) =
20400.
Required perecentage=
11628
20400
??????100%=57%
02-03-2015
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25. PERCENTAGE IN RATIO
4.Two numbers A and B are such that the sum of 5% of A and 4%
of B is two-third of the sum of 6% of A and 8% of B. Find the ratio
of A : B. A.2 : 3B. 1 : 1 C. 3 : 4 D. 4 : 3
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5% of A + 4% of B =
2
(6% of A + 8% of B)
3
5
A +
4
B=
2
(
6
A +
8
B)
100 1003100 100
1
A +
1
B=
1
A +
4
B
20 2525 75
1
-
1
A =
4
-
1
B
2025 7525
1
A =
1
B
100 75
5% of A + 4% of B =
2
3
6%��??????+
5% of A + 4% of B = 4% of A +
16
3
% of B
1% of A =
16
3
−4%of B
1% of A =
4
3
%of B
A
=
100
=
4
.
B753
Required ratio = 4 : 3

26. PERCENTAGE IN ALGEBRA
7.TwotailorsXandYarepaidatotalofRs.550perweekbytheir
employer.IfXispaid120percentofthesumpaidtoY,how
muchisYpaidperweek?
A.Rs. 200B. Rs. 250 C.Rs. 300D.Noneof these
Let the sum paid to Y per week be Rs. z.
Then, z + 120% of z = 550.
�+
120
100
�=550.
220
100
�=550.
Z = 550X
100
220
=250.
02-03-2015
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[email protected]
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27. PERCENTAGE IN ALGEBRA
8.GauriwenttothestationersandboughtthingsworthRs.25,
outofwhich30paisewentonsalestaxontaxablepurchases.If
thetaxratewas6%,thenwhatwasthecostofthetaxfree
items?
A. Rs. 15 B. Rs. 15.70 C. Rs. 19.70D. Rs. 20
6% of taxable =
30
100
.
Cost of taxable =
30
100
??????
100
6
=5.
Cost of tax free items = 25 –5 = Rs.20.
02-03-2015
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28. PERCENTAGE IN ALGEBRA
12.Twostudentsappearedatanexamination.Oneofthem
secured9marksmorethantheotherandhismarkswas56%of
thesumoftheirmarks.Themarksobtainedbythemare:
A. 39, 30B.41, 32 C. 42, 33D.43, 34
One student secured 44% of the sum of marks.
Second student secured 56% of the sum of marks.
Difference = 12% of the sum of marks = 9 marks.
Sum of marks =
100
12
??????9=75.
Hence first scored
44
100
??????75=33 and second scored = 42.
02-03-2015
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29. PERCENTAGE IN RACES & GAMES
11.Abatsmanscored110runswhichincluded3
boundariesand8sixes.Whatpercentofhistotalscore
didhemakebyrunningbetweenthewickets?
A.45% B.45
5
11
%C.54
6
11
%D.55%
Total runs not by running = 3x4 + 8x6 = 12+48=60.
Percent of his total score he made by running =
60
110
??????100=54
6
11
%
02-03-2015
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[email protected]
29

30. 13.Afruitsellerhadsomeapples.Hesells40%apples
andstillhas420apples.Originally,hehad:
A. 588 applesB. 600 apples
C. 672 applesD. 700 apples
60% of apples = 420.
Originally he had =
100
60
??????420
=700 apples.
02-03-2015
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[email protected]
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31. PERCENTAGE IN NUMBER SYSTEM
14.Whatpercentageofnumbersfrom1to70have1or9inthe
unit'sdigit?A.1 B.14C.20D.21
numbers from 1 to 70 that have 1 or 9 in the unit's digit are
1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
Required percentage =
14
70
X100
=20%
02-03-2015
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[email protected]
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32. PERCENTAGE IN NUMBER SYSTEM
15.If A = x% of y and B = y% of x, then which of the following is true?
A. A is smaller than B.B. Relationship between A and B cannot be determined.
C. A is greater than B D. If x is smaller than y, then A is greater than B.
E. None of these
A = x% of y
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32
=
�
100
??????�=
��
100
=
��
100
=
�
100
??????�= y% of x
= B.

33. PROFIT & LOSS
C.S.VEERARAGAVAN
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34. 02-03-2015
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35. 02-03-2015
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36. Profit & Loss
Therearetwoshopkeepershavingshops
sidebyside.
Thefirstshopkeepersellsbicycles.
Hesellsabicycleworth$30for$45.
Onedayacustomercomesandbuysa
bicycle.
Hegivesa$50notetotheshopkeeper.
Theshopkeeperdoesn'thavechangesohe
goestothesecondshopkeeper,getsthe
changefor$50,andgives$5andthe
bicycletothecustomer.
Thecustomergoesaway.
Thenextdaythesecondshopkeepercomes
andtellsthefirstshopkeeperthatthe$50
noteiscounterfeitandtakeshis$50back.
Now,howmuchdoesthefirstshopkeeper
lose?
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Fromthesecondshopkeeperhetook
$50andgaveback$50sotherewasno
profitnoloss.Tothecustomerhegave
$5+$30bicycle.Therefore,histotal
lossis$35

37. PROFIT / LOSS
Ifamanpurchase11orangefor
Rs10andsellthem10forRs
11.Howmuchprofitorlossdid
hemade?
Profit or loss made =
11??????11−10??????10
10??????10
X100 =21% profit.
If'a'articlesareboughtforRs
'b'andsellthem'c'forRs'd'.
Thenprofitorlossmadebythe
vendor:
��−��
��
�100
02-03-2015
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USUAL METHOD
C.P of 11 oranges Rs.10
C.P of 1 orange is Rs.
10
11
.
S.P of 10 oranges Rs.11
S.P of 1 orange is Rs.
11
10
Profit or loss made
=
�.�−??????.�
??????.�
??????100
=
11
10
−
10
11
10
11
??????100
=
11??????11−10??????10
110
??????
11
10
??????100
=
11??????11−10??????10
10??????10
??????100

38. Example 2
Aboybuysorange9for
Rs.16andsellthem11
forRs.20.Findprofitor
losspercentage.
profit or loss percent
made :
9??????20−11??????16
11??????16
�100=
25
11
%�??????��????????????
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Did the original problem
really have so much
information in it ?
Yeeeeesssssss---
only if you go down
deep enough.
It is IMPOSSIBLE to get
to solutions like these, if
you tend to rush through
to the solution using the
most familiar ways
known to you.

39. PROFIT PERCENTAGE
Somearticleswereboughtat6articlesforRs.5
andsoldat5articlesforRs.6.Gainpercentis:
A.30%B.33
1
3
%C.35%D.44%
Gain%=
36−25
25
�100=44%
02-03-2015
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[email protected]
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40. PROFIT PERCENTAGE
Ashopkeeperexpectsagainof22.5%onhiscostprice.
Ifinaweek,hissalewasofRs.392,whatwashis
profit?
A.Rs.18.20B.Rs.70
C.Rs.72 D.Rs.88.25
C.P=
100
122.5
x392=Rs.320.
Profit=Rs.392–Rs.320=Rs.72.
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41. PROFIT PERCENTAGE
Sampurchased20dozensoftoysattherateofRs.375per
dozen.
HesoldeachoneofthemattherateofRs.33.
Whatwashispercentageprofit?
A.3.5B.4.5C.5.6D.6.5
C.Pof1toy=
375
12
=31.25
S.P=33.
Profit%=
33−31.25
31.25
x100
=
1.75
31.25
x100=5.6%
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C.P = Rs.375 per dozen
S.P = 33 x 12 = Rs.396
Profit % =
396−375
375
x100
=
21
375
x 100
=
28
5

42. PROFIT PERCENTAGE
AlfredbuysanoldscooterforRs.4700andspendsRs.
800onitsrepairs.
IfhesellsthescooterforRs.5800,hisgainpercentis:
A.4
4
7
% B.5
5
11
%C.10% D.12%
CostPrice(C.P.)=Rs.(4700+800)=Rs.5500.
SellingPrice(S.P.)=Rs.5800.
Gain=(S.P.)-(C.P.)=Rs.(5800-5500)=Rs.300.
Gain%=
300
5500
??????100=5
5
11
%
02-03-2015
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42

43. PROFIT PERCENTAGE
Ifsellingpriceisdoubled,theprofittriples.
Findtheprofitpercent.
A.66
2
3
B.100 C.105
1
3
D.120
LetC.Pbex.S.P=y.Profit=y–x.
Given3(y–x)=2y–x.
Y=2x.
Profit%=
y−x
x
??????100=
x
x
??????100=100.
02-03-2015
VEERARAGAVAN C S, APTITUDE TRAINER,
[email protected]
43

44. PROFIT PERCENTAGE
Inacertainstore,theprofitis320%ofthecost.Ifthe
costincreasesby25%butthesellingpriceremains
constant,approximatelywhatpercentageoftheselling
priceistheprofit?
A.30% B.70% C.100% D.250%
LetC.P.=Rs.100.Then,Profit=Rs.320,S.P.=Rs.420.
NewC.P.=125%ofRs.100=Rs.125
NewS.P.=Rs.420.
Profit=Rs.(420-125)=Rs.295.
Profit%=
295
420
x100=
59
84
x100≈
60
84
x100=
500
7
=70%.
02-03-2015
VEERARAGAVAN C S, APTITUDE TRAINER,
[email protected]
44