### PROBLEMS ON AGES PERCENTAGES ARTHIMETIC MATERIAL

#### PROBLEMS ON AGES PERCENTAGES ARTHIMETIC MATERIAL                                                                                         PROBLEMS ON AGES

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

EG:

Five years ago laxmi's age was seven times the age of her son at that

time and after 5 years her age will be thrice the age of her son. how old is laxmi now?

5 years ago  7 :1

5 years after 3:1

7x+10 = 3

........  ...

x+10    1

7x+10 = 3x+30

4x = 20

x = 5

7*5 = 35+5 = 40

METHOD 2:

7 : 1

(3:  1)3

7 : 1

9 :  3

2PARTS INCREASED

AFTER 5 YEARS BEFORE 5 YEARS 5 TOTAL 10

2P =10

P = 5

(5*7)+5 = 40

EG:

SANDHYA GOT MARRIED 4 YEARS AGO TODAY HER AGE IS 1(1/8) TIMES HER  AGE AT THE TIME OF MARRIAGE

HER SONS AGE IS 1/12 OF HER AGE WHAT IS THE AGE OF SANDHYAS AGE?

PRESENT AGE = X

MARRIAGE AGE = X-4

X =  1(1/8)(X-4)

8X = 9X - 36

X = 36

(1/12) *36 = 3 YEARS

METHOD 2:

9 :8

1P = 4

4*9  = 36

(1/12) *36 = 3 YEARS

EG3:

MOHAN GOT MARRIED 9 YEARS AGO TODAY HIS AGE IS 1(1/3) TIMES HIS AGE AT THE TIME OF MARRIAGE FIND HIS

PRESENT AGE?

4 : 3

1P = 9

4*9 = 36

EG:

MADHU GOT MARRIED 6 YEARS AGO TODAY HER AGE IS 125% TIMES HER AGE AT THE TIME OF MARRIAGE

HER SONS AGE IS ONE TENTH OF HER AGE?

HER SONS AGE IS?

125%

125 :  100

5  : 4

MADHU GOT MARRIED 6 YEARS AGO

1P  =6

SO 5*6  =30

HER SONS AGE IS ONE TENTH OF HER AGE (1/10)*30 = 3 YEARS

EG:

AGES OF 3 PERSONS ARE IN THE RATIO 5 : 7 :9 SUM OF SQUARES OF THE AGES OF PERSONS EXCLUDING THAT

OF YOUNGEST PERSON IS 3250 WHAT WILL BE THE RATIO OF THEIR AGES AFTER 10 YEARS?

7 x^2 +9 x^2 = 3250

16 x^2 = 3250

x^2 = 3250/16

EG:

IN 10 YEARS THE AGE OF ROHIT WILL BE 3 TIME THAT OF HIS AGE 6 YEARS AGO WHAT IS THE PRESENT AGE?

NOW X

AFTER X+10

X+10 = 3(X+6)

2X = 28

X = 14

EG:

RAM WILL BE 5 TIMES AS OLS AS HE IS NOW AFTER 8 YEARS HOW MANY YEARS HENCE WILL BE 10 TIMES

AS OLD AS HE IS NOW?

PRESENT AGE = X

AFTER 8 YEARS =  X+8

X+8 = 5X

X= 2

10*2 = 20YEARS

20-2  =18 YEARS

EG:

RAKESH IS 30 YEARS YOUNGER THAN HIS AUNT TODAY FIVE YEARS AGO RAKESH WAS (1/4) AS OLD AS HIS AUNT

HOW OLD WILL RAKESH AUNT BE 8 YEARS HENCE?

5 YEARS AGO   1:  4

3P =30

P =10

10*4 = 40 + 5 =  45+8=    53

EG:

SAMPATH IS AS MUCH YOUNGER TO VAMSI AS HE IS OLDER TO RAKESH IF THE SUM OF THE AGES OF VAMSI AND RAKESH IS 56 YEARS HOW OLD IS

SAMPATH NOW?

R      S         V

SAME DIFFERNCE

IF A,B,C ARE IN AP

B= (A+C)/2

56/2 = 28

EG:

P IS AS MUCH YOUNGER TO Q HE IS OLDER TO R IF THE SUM OF THE AGES OF Q AND R IS 50 YEARS

WHAT IS THE DIFFERENCE BETWEEN AGES OF P AND Q?

P,Q,R IN A P

(P+Q)/2

50/2

25

EG:

SAHITHI'S AGE IS (1/6) TH OF HER FATHERS AGE SAHITHIS FATHER AGW WILL BE TWICE OF KAMALS AGE

AFTER 10 YEARS . IF KAMALS 8 TH BIRTHDAY WAS CELEBRATED TWO YEARS AGO THEN WHAT IS SAHITHIS PRESENT AGE?

8 YEARS KAMAL

8 +2 = 10 YEARS PRESENT

AFTER 10 YEARS 20

HIS FATHER DOUBLE

40  : 20

PRESENT FATHER AGE

40-10

30

(1/6)*30

5 YEARS

EG:

3 YEARS AGO THE FATHERS AGE WAS TWICE THE AGE OF HIS FOUR DAUGHTERS IN 3 YEARS TIME THE AGE OF

HIS FOUR DAUGHTERS.IN 3 YEARS TIME THE FATHERS AGE WILL BE EQUAL TO SUMOF AGES OF THE DAUGHTERS

FIND THE PRESENT AGE OF FATHER?

FATHER       4 DAUGHTERS

2X               X

1                  1

2X+6                X+24

2X+6  =   1

.....     .....

X+24       1

2X+6 =  X+24

2*18 = 36

PRESENT = 36 +3

= 39

EG:

WHEN I ADD 4 TIMES MY AGE 4 YEARS FROM NOW TO 5 TIMES MY AGE 5 YEARS FROM NOW I GET

10 TIMES MY PRESENT AGE HOW OLD I WILL BE 3 YEARS FROM NOW?

PRESENT AGE  X

4(X+4) + 5 (X+5)  = 10X

X = 25+16

= 41

AFTER 3 YEARS = 44 YEARS

EG:

THE RATIO OF AGES OF A MOTHER AND HIS SON IS 2 :1 MOTHER WAS 24 YEARS OLD WHEN SHE GAVE

BIRTH TO HER ONLY DAUGHTER WHO IS 6 YEARS YOUNGER TO HER ONLY SON FIND THE PRESENT AGE OF

36 ,18

EG:

WHEN I WAS MARRIED 10 YEARS AGO MY WIFE IS THE 6TH MEMBER OF THE FAMILY TOADY MY FATHER DIED AND A BABY BORN TO ME THE AVERAGE AGE OF MY FAMILY

A BABY BORN TO ME THE AVERAGE AGE OF MY FAMILY DURING MY MARRIAGE IS SAME AS TODAY WHAT IS THE AGE OF FATHER WHEN DIED?

MARIAGE AGE             =        PRESENT AGE

F+ X1+X2+X3+X4+X5 =  (X1+X2+x3+X4+X5+50)+0

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

6                       6

F = 50

10 YEARS AGO = 50

PRESENT  = 60

EG:

THE AGE OF THE TWO FRIENDS WERE IN THE RATIO OF  6 :5 IF THE SUM OF THEIR AGES IS 55 THEN AFTER

HOW MANY YEARS THEIR AGES WILL BECOME  8 :7

11P = 55

P =5

2*5 = 10

EG:

THE SUM OF THE AGES OF SUNIL AND HIS FATHER IS 46 YEARS 3 YEARS BACK FATHERS AGE WAS 4 TIMES SUNILS AGE FIND PRESENT AGE OF SUNIL?

S+F  =46

3 YEARS AGO   =40 YEARS

AT THAT TIME  4 :1

5P = 40

P = 8

8 +3 = 11

EG:

AFTER 30 YEARS A'S AGE IS 3 TIMES TO THE PRESENT AGE THEN FIND A AGE?

PRESENT AGE  X

X+30  = 3X

2X = 30

X = 15

EG:

THE  RATIO OF THE AGES OF MR RAO AND HIS SON I1 6 : 1 AFTER 5 YEARS THE RATIO WILL BE 7 :2

WHAT WILL BE THE AGE OF MR RAO?

6 :1

7 : 2

1 PAR 5 YEARS

5*6

30 YEARS

EG:

THE AGES OF A FATHER AND HIS DAUGHTER ARE IN THE RATIO  4: 1 IF 5 YEARS AGO THEIR AGES WERE IN THE

7 :1 FIND THE AGE OF FATHER AND PARENT?

4 :1

7 :1

MULTIPLE 1ST EQUATION WITH1 ( 4 :1) 2 = 8 : 2

7 : 1

1 PART = 5

5*6 = 30

EG:

5 YEARS AGO LAKSHMI'S AGE WAS 7 TIMES THE AGE OF HER DAUGHTER AT THE TIME AFTER 5 YEARS HER AGE WILL BE

THRICE THE AGE OF HER DAUGHTER HOW OLD NOW?

7  :  1

(3 :1 )3

7 :1

9 :3

2P =10

P = 5

7*5 = 35

NOW 35+5 = 40

EG:

MR KRANTHI IS 4 TIMES AS OLD AS BINDU  3 YEARS HENCE THE SUM OF THEIR AGES WILL BE 41 YEARS

WHAT IS THE AGE OF KRANTHI?

4X  : X

4 : 1

+ 3 YEARS = 41

MINUS     6

...........

35

5PARTS  ----------- 35

1 PART ..........?

ANS  28

EG:

PHANI IS AS MUCH YOUNGER TO MICHAEL AS HE IS OLDER TO RAMESH IF THE SUM OF THEIR AGES OF

MICHAEL AND RAMESH IS 48 YEARS FIND THE AGE OF PHANI?

V- P  =  P-R

V+ R = 48

V+R = 2P

2P = 48

P =24

EG:

THE SUM OF THE AGES OF RAMANA AND RAJESH IS 56 YEARS 6 YEARS AGO THE RATIO OF THE AGES WAS 7 :4 HOW OLD IS MR RAJESH NOW ?

RAM+RAJ = 56

7 :4

-6 *2 = -12

56

-12

....

44

7 :4

11P = 44

P =4

6 YEARS BACK  = 4 *4 = 16

+6 =  16 +6 = 22

EG:

IN 8 YEARS THE AGE OF RAHUL WILL BE  4 TIMES THAT OF HIS AGE 13 YEARS AGO WHAT IS THE PRESENT AGE?

RAHUL

X+8          X-13

(X+8)  =  4(X-13)

3X = 60

X = 20

EG:

THE PRESENT AGE OF PRANATHI IS TWICE THE AGE OF SARADA 3 YEARS AGO IF PRANATHI IS 2 YEARS OLDER TO SARADA WHAT IS THE PRESENT AGE OF PRANATHI?

P,S

3  YEARS AGO = S-3

P 2(S-3)

P = S+2

P-2 = S

P = 2(P-5)

P = 10

EG:

A MOTHER HAD 3 SONS THEY WERE BORN AT AN INTERVALS OF 3 YEARS THE TOTAL AGE OF 3 SONS IS 24 YEARS WHAT IS THE AGE OF YOUNGEST

SON?

X+X+3+X+6  = 24

3X+9 = 24

3X = 15

X =5

EG:

NEELIMA GOT MARRIED 4 YEARS AGO TODAY  HER AGE IS 1(1/6) TIMES THE AGE AT THE TIME OF HER MARRIAGE HER SONS AGE IS

(1/14) OF HER AGE WHAT IS THE AGE OF NEEELIMA'S AGE?

(X-4) (1(1/6)) =X

(X-4)(7/6) = X

X =  28

(1/14)*28 = 2

EG:

THE RATIO OF THE PRESENT AGES OF TWO BROTHERS IS 1 :2 AND 5 YEARS BACK THE RATIO

WAS 1 :3 WHAT WILL BE THE RATIO OF THEIR AGES AFTER 5 YEARS?

1 : 3

1  : 2

(1:2) 2 = 2 :4

1 :3

2 :4

AFTER FIVE YEARS +1 TO RATIO = 3 : 5

EG:

THE RATIO BETWEEN THE SCHOOL AGES OF NEELAM AND SHYAM IS 5 :6 RESPECTIVILY  IF THE RATIO BETWEN

ONE THIRD AGE OF NEELAM AND HALF OF SHYAMS AGE IS 5 :9

THEN WHAT IS THE SCHOOL AGE OF SHYAM?

N :S

5: 6

N/3 : S:2

(1/3)5   : (1/2)6

(5/3) : 3

EG:

A MAN IS 24 YEARS OLDER THAN HIS SON IN TWO YEARS HIS AGE WILL BE TWICE THE AGE OF HIS SON

FIND THE AGE OF HIS SON?

F -S = 24

F : S

2  :1

1P = 24

-2

.....

22

EG:

THE AGES OF A AND B ARE IN THE RATIO 4 :1 THE PRODUCT OF THEIR AGES IS 64

WHAT WILL BE THE RATIO OF THE AGES AFTER  4 YEARS?

A: B = 4 :1

4X,X

(4X) (4X) = 64

X= 4

EG:

RAJESH WAS N YEARS OLD X YEARS AGO HIS AGE M YEARS FROM NOW WOULD BE EXPRESED AS?

N+M+X

EG:

THE RATIO BETWEEN THE PRESENT AGES OF A AND B IS 5 :3 RESPECTIVILY

THE RATIO BETWEEN THE A'S AGE 4 YEARS AGO AND B'S AGE 4 YEARS HENCE IS 1 :2

WHAT IS THE RATIO BETWEEN  A'S AGE 4 YEARS HENCE AND B'S AGE 4 YEARS AGO?

A : B = 5 :3

(5X-4)/(3X+4) = 1/1

X = 4

5X = 20

20 : 12

+4      -4

24 : 8

3 :1

EG:

A PERSONS PRESENT AGE IS 2/5 TH OF THE AGE OF HIS MOTHER AFTER 8 YEARS HW WILL BE ONE HALF OF THE AGE OF HIS MOTHER

HOW OLD IS THE MOTHER AT PRESENT?

PERSON            MOTHER

(2/5 ) X                 X

2   :  5

AFTER 8 YEARS

1 :2

(1 :2 ) 3

3 : 6

2 :5

3 :6

1 PART = 8 YEARS

5*8 =40 YEARS

eg:

RAHUL MARRIED 4 YEARS AGO NOW HIS AGE IS 1(1/8) TIMES AT THE TIME OF HIS MARRIAGE NOW HIS PRESENT AGE?

1(1/8) (X-4) = X

X = 36

OR

9 :8

1 PART 4 YEARS

9 PARTS 36 YEARS

EG:

SHARMA MARRIED 6 YEARS AGO NOW HIS AGE 1(1/3) TIMES AT THE TIME OF HIS MARRIAGE THEN TIND HIS PRESENT AGE?

4/3(X-6) = X

X = 24

OR

4 : 3

1 PAR T 6

4 *6 = 24

EG:

AHUJA MARRIED 7 YEARS AGO NOW HIS AGE 125 % AT THE TIME OF HIS MARRIAGE THEN FIND HIS AGE?

(X-7 ) (125/100)  = X

5X - 35 = 4X

X = 35

EG:

PRESENT RATIO OF THE AGES OF A AND B IS 3 :4 AFTER  6YEARS THEIR AGES RATIO 4 :5

THEN FIND PRESENT AGE RATIO?

3 : 4

4 : 5

1 PART INCREASED

6 YEARS

3 PARTS = 3 *6  = 18 YEARS

EG :

PRESENT RATIO OF AGES OF A AND B IS 3 : 5 AFTER 10 YEARS THEIR AGES ARE IN THE RATIO  5 :7

THEN FIND PRESENT AGE?

3 : 5

5 :7

2 PARTS INCREASED

PART = 5

3 PARTS  = 15

5 PARTS = 25

EG:

PRESENT RATIO OF THE AGES OF A AND B IS 5 :7

AFTER 5 YEARS THEIR RATIO WILL  BE CHANGED TO 3 :4 THEN FIND PRESENT RATIO OF THEIR AGES?

(5X+5/7X+5) = 3/4

(5X+5)4 = 3(7X+5)

X =5

A   = 5*5

B = 35

OR

5 :7

3 :4

5 :7

2(3) : 2(4)

5 : 7

6 :8

1 PART = 5

7 PARTS = 35

EG:

PRESENT FATHER IS 7 TIMES TO SONS AGE

AFTER 10 YEARS FATHER AGE IS 3 TIMES TO HIS SONS AGE

THEN FIND FATHER AGE?

FATHER          SON

7                1

AFTER 10 YEARS3 TIME SO MULTIPLE WITH 3

(3 : 1)3

9 :3

7 :  1

9 :3

2P = 10

P = 5

7X = 7 *5 = 35

EG:

5 YEARS BACK RATIO OF THE AGES OF A AND B IS  4 : 7

AFTER 7 YEARS  A AND B AGES RATIO IS 2:3

THEN FIND THEIR AGES?

5 YEARS BACK   4 :7

7 YEARS LATER   2 :3

5 YEARS BACK + 7 YEARS LATER  = 12

(4X+12/7X+12) = (2/3)

X = 6

A = 4X = 24

B = 7X = 42

NOW AGES

24 + 5 = 29

42 +5  =47

METHOD 2:

5 YEARS BACK  4 :7

7 YEARS LATER  6 :9

2 PARTS  12

1 PART = 6

EG:

3 YEARS BACK FATHER AGE IS DOUBLE TO TOTAL AGES OF HIS 4 SONS

AFTER 4 YEARS  FATHER AGE IS DOUBLE TO TOTAL AGES OF HIS 4 SONS

FATHER       4 SONS

2              1

2X           X

3  YEARS LATER       2X +6    X +24

2X+6 = X+24

X +18

2X = 2*18

= 36

AFTER 3 YEARS  36 +3 = 39 YEARS

EG:

PRESENT DIFFERENCE BETWEEN A AND B AGES IS 12 YEARS

AFTER 10 YEARS  AND B AGES RATIO IS 5 :7

THEN FIND PRESENT AGES?

10 YEARS LATER  5 :7

( 7 -5) =2 PARTS

2 PARTS = 12

= 6* 5

30

7*6   = 42

PRESENT

30 -10      42-10

20           32

EG:

PRESENT AGES OF A AND B IS 50 YEARS

AFTER 5 YEARS THIER AGEIR AGES RATIO IS 2 :3 THEN FIND PRESENT AGES?

PRESENT TOTAL = 50 YEARS

AFTER 5 YEARS = 60 YEARS

]        5P = 60

P =12

2 :3

2*12 : 3 *12

24 : 36

'

PRESENT 24- 5 =19

B = 36-5 =29

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 = 1/2

1/2 = 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

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

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%

39         21

plus 10 LITER MILK 10

39+10

49            21

(21/70)* 100 =30%