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
MOTHER AD SON (IN YEARS)
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
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%
39 21
plus 10 LITER MILK 10
39+10
49 21
(21/70)* 100 =30%
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