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 = 1/2
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%
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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