### HOME TUITION CAPSULE ON QUANTITATIVE APTITUDE PERCENTAGES MATERIAL

### PERCENTAGES :

###
To convert percentage into fractions divide the given value with hundred

To convert fraction into percentage multiple the given fraction with 100%

50% = 50/100 = 1/21/2 = 1/2(100%) = 50%

EX:

convert the folowing percentages into fraction

1) 60% = 60/100 = 3/5

2) 12.5 % = 12.5/100 = 5/40 = 1/8

3) 33 (1/3)% = 100/3 = 1/3

4) 16(2/3)% = 50/(3*100) = 1/6

EX:

convert the following fractions into percentage

1) (3/4)*100 = 75 %

2) (4/5) * 100 = 80%

3) (2/3) * 100 = 200/3 = 66(2/3)%

4) (1/5) *100 = 20%

5) (1/12)*100 = 25/3 % = 8 (1/3)%

NOTE:

50% = 1/2

25% = 1/4

12(1/2)% = 1/8

6(1/4)% = 1/16

66 (2/3)% = 2/3

33(1/3)% = 1/3

16(2/3) % = 1/6

8(1/3)% = 1/12

75% = 3/4

14 (2/7)% = 1/7

11(1/9)% = 1/9

9 (1/11)% = 1/11

NOTE:

1/1 = 100%

1/2 = 50%

1/3 = 75%

1/4 = 25%

1/5 = 20%

1/6 = 16 (2/3)%

1/7 = 14(2/7)%

1/8 = 12(1/2)%

1/4 = 11(1/4)%

1/10 = 10%

1/11 = 9(1/11)%

1/12 = 8(1/3)%

FORMULAE:

1 x%y = (x/100)y

(xy)/100

2 x is what percentage of y

what = (100%x)/y

is/of just remember

EG:

IN 250 FIND 30 % VALUE?

10% = 25

30 % = 75

EG:

IN 360 FIND 15%

10% = 36

5% = 18

15% = 54

EG:

IN 450 FIND 22 % VALUE?

10% = 45

20% = 90

2% = 9

......

99

IN 240 FIND 19%?

20% 48

-1% 2.4

........

45.6

EG:

30 % OF 120 = 36

EG:

IN A CLASS BOYS AND GIRLS ARE IN THE RATIO 3:2 then find percentage of boys

total 5 parts

boys (3/5) * 100 = 60%

girls (2/5) *100 = 40%

METHOD 2

5 - 100

2 ?

5---100

3 ?

EG:

IN A CLASS BOYS AND GIRLS ARE IN THE RATIO 3:2 then find percentage of boys

boys what percentage more that girls?

(1/2) * 100 = 50%

EG:

IN A CLASS BOYS AND GIRLS ARE IN THE RATIO 3:2 then find percentage of boys

girls what percentage more than boys ?

(1/3)* 100 = 33(1/3)%

EG:

IN A CLASS BOYS AND GIRLS ARE IN THE RATIO 3:2 then find percentage of boys

Boys is what percentage of girls?

(3/2)100 = 150%

EG:

IN A CLASS BOYS AND GIRLS ARE IN THE RATIO 3:2 then find percentage of boys

girls is what percentage of Boys ?

(2/5)*100 = 200/3 = 66(2/3) %

MODEL :

EG:

A Salary is 20 % less than b salary then b salary is what % more than a salary?

4 : 5

(1/4) 100 = 25%

short cut formulae

(X/(100±X))*100%

MORE - PLUS

DECREASE OR LESS -- MINUS

COMPARE ABOVE PROBLEM

(20/(100-20))*100

(20/80)*100 = 25%

EG:

A rectangle length increased by 10 % by what percentage breadth has to be decrease sothat no change in its area?

(10/(100+10))*100

(10/110)*100

9(1/11)%

EG:

price of a article decreased by 30% by what percentage it sales has to be increase so that these is no effect in revenue?

(30/70)*100

300/7

42(6/7)%

EG:

price of a sugar increased by 20% by what percentage it consumption has to be decreased sothat there is no change

(20/120)*100%

16(2/3)%

MODEL:

EG:

Population of a town is 5000 in the first year it is increased by 10 % and then 2nd year it decreased by 20 % find the

find the population after 2 years and the overall percentage

population first year 10% increased so 110/100

population second year 20% decreased 80/100

5000 *(110/100) * (80/100)

550*8

4400

(600/5000)*100

12% decreased

METHOD 2:

+10% -20%

ONLY ON TWO PERCENTAGE CHANGES ONLY

((X+Y+(XY/100)) %

(10-20-200/100)%

-12% DECREASED

EG:

A rectangle length is decreased by 10% and bredth decreased by 10 %

find the effect on its area?

(-10-20+(200/100)%

-28% decrease

EG:

thrice of a article first increased by 10% and again increased by 20 % then decrease by 25 %?

100*(110/100)* (75/100)

99%

1 percentage decreased

MODEL 3:

EG:

population of a town first increased by 10 %and then decreased by 205 if the final population is 4400 initial population?

increased by 10% so 100/110

decreased by 20% so 100/80

4400*(100/110)*(100/80)

5000

EG:

A man spends 85% of his income per household items and out of the remaining 50% per transport if he finally saves 900 find his income?

900*(100/15)*(100/50)

12500

EG:

In a college 30% are arts graduates out of the remaining 40% are science graduates out of the remaining 50% are computer

graduates find total no of students?

-30% -40% -50%

210*(100/70)*(100/60)*(100/50)

EG:

The ratio between a ,b,c is 3 :4 :5 a increased by 20% and b increased by 25% and c reduced by 10% then find new ratio?

300 : 400 : 500

360 : 400 : 500

36 : 50 :45

EG:

Total votes polled in a election is 1200 votes difference between the winning and loosing candidate is 20%

then find how much votes that winning candidate got?

100%

20% 80%

differcnce 60% = 1200

1% = 20 votes

80% = 1600 votes

EG:

IN A ELECTION BETWEEN TWO CANDIDATES ONE CANDIDATE GOT 60% VOTES AND WON BY 500 VOTES THEN FIND TOTAL VOTES?

100%

40% 60%

DIFFERENCE 20% = 500

1% = 25 VOTES

TORAL = 100*25 = 2500 VOTES

EG:

TO pass in an exam every guy need 40% marks but one candidate got 40 marks and then failed by 40 marks then

total marks in that exam?

pass : 40 + 40

80

so pass percentage 40% = 80marks

1% = 2 marks

100% = 200 marks

EG:

to pass in an exam students need 30 % marks but one student got 100 marks

he got 10 marks more than pass mark then total marks in that exam?

pass % pass marks

30% 100marks - 10 marks

30% 90 marks

1% 3 marks

100% = 300 marks

Eg

in an exam a got 32% marks and failed by 9 marks

b got 40% marks and pass by 15 marks then find total marks in that exam?

a 32% -9marks

b 40% 15 marks

difference 15-(-9)

24

8% 24 marks

1% ?

1 percent 3 marks

total marks 300

Percentage:

percentage literally means every hundred

comparing every quantity with respectto t100 is called percentage

25% = 1/4

a percentage can be expressed in fraction

25% = 1/4

in aratio = 1:4

and also in a decimal form .25

conversions:

percentage can be converte into fraction by dividing with hundred

45% = 45/100 = 9/20

a fraction can be converted into percentage by multiplying with 100

(3/4)*100 = 75%

60% = (60/100) = 3/5

(4/5) = (4/5)*100 = 80

10 interms of percentage

10*100 =1000%

EG :

38 IS WHAT PERCENT OF 152

152 ------------ 100

38 ?

EG:

WHAT PERCENTAGE IS 50 OF 40

IS/OF *100

EG:

30% OF A NUMBER IS 60

30............60

100.........?

EG:

20% OF A NUMBER IS 16

100% OF A NUMBER IS 80

EG:

32% OF A NUMBER EXCEEDS 12% OF THE SAME BY 60 WHAT IS THAT NUMBER?

32% - 12% = 20%

20% ----------------60

100%.....................?

60*5 = 300

EG:

A NUMBER WHEN INCREASED BY 30% GIVES 780

FIND HUNDRED PERCENT OF NUMBER?

A NUMBER INCREASED BY 30% SO 130%

130% NUMBER IS 780

100 %..........?

(780*100)130

600

EG:

A NUMBER WHEN DECREASED BY 12% OF IT IT GIVES 220 FIND NUMBER?

DEC BY 12% SO 100-12 =88%

88%----------220

100% ............?

(100*220)/88

250

EG:

PRECENTAGE INCREASE = (INCREASE/INITIAL)*100

PERCENTAGE DECREASE = (DECREASE/INITIAL)*100

EG:

THE NUMBER OF STUDENTS IN A SCHOOL IS DECREASED TO 320 FROM 400 WHAT IS THE PERCENT DECREASED

(320/400)*100 = 80

SO 100-80 = 20%

EG:

RAVI SPENDS 76% OF HIS SALARY WHAT HE SAVING IF HIS TOTAL SALARY IS 4000

76% ---------- 3040

4000

3040

...........

960

EG:

IN AN ELECTION BETWEEN TWO CANDIDATES A CANDIDATE GOT 38 % OF VOTES POLLED AND LOST TO HIS RIVAL BY 3600 VOTES FIND TOTAL?

100

62 38

62-38 = 24%

24% - 3600

100%--?

EG:

IN AN ELECION BETWEEN A AND B A GOT 60% OF VOTES WON BY MAJORITY OF 1800 VOTES FIND THE TOTAL NUMBER OF VOTES POLLED?

100

60% 40%

20% ------------1800

100% ........?

1800 *5 = 9000

EG:

IN A SCHOOL OF 300 STUDENTS 70% OF STUDENTS BOYS

20% OF THE BOYS ARE ABSEST THEN HOW MANY BOYS ARE PRESENT?

BOYS = 70% OF TOTAL ABSENT 20% OF BOYS

20% OF 70% OF TOTAL

14% OF TOTAL

(14/100)*300

42

EG:

IN A SCHOOL OF 300 STUDENTS BOYS ARE 70%

IF 30% OF GIRLS ARE ABSENT FIND THE TOTAL NUMBER OF GIRLS PRESENT?

70% = 210

300 - 210 =90

30% OF GIRLS ABSENT

SO 30% OF 80 = 27

90-27 = 63

EG:

IN A SCHOOL OF 400 STUDENTS 40% ARE GIRLS 30% OF THE BOYS AND 50%OF THE

GIRLS FAILED IN AN EXAM EHAT PERCENTAGE OF THE STUDENTS IN A SCHOOL PASSED THE EXAM?

TOTAL 100 PERCENT

100

60 40

18 42 20 20

42 +20 = 62%

EG:

A STUDENT HAS TO GET 38% OF MARKS TO PASS THE EXAMINATION ARUN GOT 81 MARKS BUT FAILED BY 14 MARKS FIND THE MAXIMUM MARKS IN AN EXAM?

38% = 81+14 = 95

38% ------95

100%........?

(100*95)/38

250

EG:

A STUDENT HAS TO GET 44% OF MARKS TO PASS THE EXAMINTION RAMYA GOT 143 MARKS WHICH ARE

33 MARKS MORE THAN NECESSARY TO PASS THE EXAM?

44----------110

100------?

(100*110)/44

250

EG:

60 LITERS OF A MIXURE WHICH CONTAINS MILK AND WATER HAVE 35% OF WATER IF 10 LITERS OF MILK IS ADDED

WHAT WILL BE THE PERCENTAGE OF WATER IN THE RESULTANT MIXURE?

60

35% 65%

21 39

plus 10 LITER MILK 10

39+10

49 21

(21/70)* 100 =30%

EG:

20 liters of mixure of wine and water contains 40% of water when 5 liters of wine is adda what

what will the percentage of wine in that mixure?

20

water wine

40% 60%

8 12

five liters added 5

..............

17

25 .........100

17...........?

(17*100)/25

68%

EG:

THE PRICE OF VIDEO IS DECREASED BY 10% THEREBY IT SALES INCREASED BY 20%

WHAT IS THE PERCENTAGE CHANGE IN TOTAL TURN OF A SHOPKEEPER?

100*(90/100)*(120/100)

108

8% INCREASE

EG:

WHEN THE PRICE OF PETROL IS INCREASED BY 20% ITS CONSUMPTION DECREASED BY 20%

FIND THE NET EFFECT ON TOTAL EXPENDITURE?

100*(120/100)*(80/100)

96%

4 PERCENTAGE DECREASE

EG:

THE PRICE OF SUGAR INCREASED BY 25% BY WHAT PERCENTAGE THE CONSUMPTION MUST BE REDUCED TO MAKE THE EXPENDITURE ON SUGAT RAMIN CONSTANT?

(X/(100±X))*100

20%

EG:

IF A SALARY IS 25% MORE THAN B THEN WHAT PERCENTAGE OF B SALARY LESS THAN A?

+25%

A B

125 100

100 ?

(100*100)/125

80

ANS : 20%

METHOD 2 :

(25/125)*100

20%

EG:

X INCOME IS 25 % LESSTHAN Y S INCOME BY WHAT PERCENTAGE Y'S INCOME IS MORE THAN X INCOME?

X Y

75 100

100 ?

(100*100)/75

33(1/3)%

METHOD 2 :

(25/75)*100

33(1/3)%

SHORTCUT FORMULAE :

LESSTHAN = (LESS/A)*100

MORETHAN = (MORE/X)*100

EG:

X AND Y ARE LESSTHAN Z BY 10% AND 20% RESPECTIVILY NOW BY WHAT PERCENTAGE

1) Z INCOME IS MORE THAN X

2) Z IS MORE THAN Y

3) X IS LESSTHAN Y

4) X IS LESSTHAN Y

5) X AND Y TOGETHER ARE MORETHAN Z

6) BY WHAT PERCENTAGE IS X OF Y IS Z OF Y

1 QUES ANS:

X Y Z

40% LESS 20% LESS 100

60 80 100

((100-60)/100)

2 QUES ANS

((100-80)/80)*100

3 QUES ANS

(20/60)*100

4 QUES ANS

(20/80)*100

5 QUES ANS

(40/100)*100

6 QUES ANS

IS/OF = (60/80) =(3/4)

(100/80) = (5/4) = 125%

EG:

X IS MORE THAN Y BY 20% AND Z IS LESSTHAN Y BY 20%

1) BY WHAT PERCENTAGE X IS MORE THAN Z

2) Z IS LESSTHAN X

3) IS X OF Z (BY WHAT PERCENTAGE)

4) OF X IS Z

X Y Z

120 100 80

1 ANS

40/80

2 ANS

40/120

3 ANS

120/80

4 ANS

80/120

EG:

B'S SALARY IS 20* MORE THAN A'S SALARY

C'S SALARY IS 25% MORE THAN B'S SALARY

D'S SALARY IS 30% MORE THAN C'S SALARY

IF A'S SALARY IS 5000 RS FIND D'S SALARY?

A B C D

20% 25% 30%

100............> 120............>150............>195

(100*50) +20 +30 (195*50)

5000 9750 25%OF 120 = 30

30 OF 150 = 45

EG:

X INCOME IS 20% MORE THAN Y'S INCOME

Y'S INCOME IS 25% MORE THAN Z'S INCOME

IF X INCOME IS 6000RS

FIND Z INCOME?

ANS : X Y Z

150<...........125<...........100

20% 25%

20% OF 125 = 25

X = 60000

150 100

(150*400) (100*400)

60000 40000

EG:

A MAN BOUGHT SOME APPLES 13% OF THEM ARE ROTTEN HE SOLD 75% OF THE BALANCE AND WAS LEFT

WITH 261 APPLES HOW MANY APPLES DID HE HAVE ORIGINALLY?

TOTAL APPLES = X

-13%........> 87% REMAINING

HE SOLD 75% REMAINING ....25%

X*(87/100)*(25/100) = 261

(261*400)/87

1200

METHOD 2 :

X

13%X 87%

75%87%X 87%25%X

= 261

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