of 20
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INDICES
The first rule: anx am= am+n
The second rule: (an)m= amn
The third rule: aman= am-n
The fourth rule: ao= 1
The fifth rule:
nmnm
1
m
n
m
m1
)a()a(a
a
1a
a
1a
If am=an, then m = n
If am= bmand m;
Then a = b if m is odd
Or a = b if m is Even
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AVERAGES
elementsofNumber
elementsofSumAverageSimple
n
nn
www
xwxwxwAverageWeighted
...
...
21
2211
naaaaMeanArithmetic n /)...( 321
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3/20
FRACTIONS AND PERCENTAGES#1 Site for Bank PO Exams
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FRACTIONS %AGE FRACTION %AGE FRACTION %AGE
1/2 50 1/8 12.5 1/14 7.14
1/3 33.33 1/9 11.11 1/15 6.67
1/4 25 1/10 10 1/16 6.25
1/5 20 1/11 9.09 1/17 5.88
1/6 16.67 1/12 8.33 1/18 5.55
1/7 14.28 1/13 7.69 1/19 5.26
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r% change can be nullified by % change in
another direction.
E.g.: An increase of 25% in prices can be nullified by a
reduction of [100x25/(100+25)] = 20% reduction in
consumption.
If a number x is successively changed by a%, b%, c%...
Final value =
The net change after two successive changes of a% and b% is
PERCENTAGES
r100
r100
...100
c1
100
b1
100
a1x
%100
abba
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5/20
PARTNERSHIP
If two partners A and B are investing their money to run abusiness then
(Simple Partnership)
If two partners A and B are INVESTINGtheir MONEYfor
different period of time to run a business then
(Compound Partnership)
BofProfit
AofProfit
BofperiodTimexBofCapital
AofperiodTimexAofCapital
BofProfit
AofProfit
BofCapital
AofCapital
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INTEREST
Amount = Principal + Interest
Simple Interest = PNR/100
Compound Interest =
Population formula P =
SI and CI are same for a certain sum of money (P) at a certain rate (r)
per annum for the first year. The difference after a period of two years is
given by
Depreciation formula = Initial Value x
SI and CI are same for a certain sum of money (P) at a certain rate (r)
per annum for the first year. The difference after a period of two years is
given by,
P100
r1P
n
n
100r1P
n
100
r1
2
2
100
PR
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PROFITAND LOSS
% Profit=
Discount % =
Effective Discount after successive discount of a%
and b% is (a + bab/100). Effective Discount
when you buy x goods and get y goods free is
100x1WeightActual
WeightActualWeightClaimed
100x
icePrMarked
icePrSellingicePrMarked
100xyx
y
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ALLIGATION
n
a
ba
mixtureofQuantity
operationnafterentityoriginalofQuantity
1
2
xx
xx
itemondsecofQuantity
itemfirstofQuantity
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SUCCESSIVE REPLACEMENT-
Where a is the original quantity, b is the quantity that is
replaced and n is the number of times the operation is
carried out,
ALLIGATION- The ratio of weights of the two
items mixed will be inversely proportional to the
deviation of attributes of these two items from theaverage attribute of the resultant mixture.
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ALLIGATIONAlligation:
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RATIO AND PROPOTION
n^krfqdpb
reqcpa
krfqdpb
reqcpa
kfdb
ecakf/ed/cb/aIf
dc
dc
ba
bathenba&
d
c
b
aIf
nnn
nnn
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TIME SPEED AND DISTANCE
Speed = Distance/Time
1 kmph = 5/18 m/sec; 1 m/sec = 18/5 kmph
If the distance covered is constant then the average speed is
Harmonic Mean of the values (s1,s2,s3.sn)
If the time taken is constant then the average speed is Arithmetic
Mean of the values (s1,s2,s3.sn)
n321
n321Avg
t....ttt
d....ddd
TakenTimeTotal
CoveredDistanceTotalSpeed
n321Avg
s/1....s/1s/1s/1
nSpeed
)speedstwofor(ss
ss2Speed
21
21Avg
n
s....sssSpeed n321Avg
)speedstwofor(2ssSpeed 21Avg
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12/20
TIME SPEED AND DISTANCE
SpeedlativeRe
eredcovbetolengthTotaltakentime,TrainsFor
Downstream/Upstream: In water, the direction along the stream is
called downstream. And, the direction against the stream is called
upstream
If the speed of a boat in still water is u km/hr and the speed of the
stream is v km/hr, then:
Speed downstream = (u + v) km/hr
Speed upstream = (u - v) km/hr
If the speed downstream is a km/hr and the speed upstream is b
km/hr, then:
hr/km)ba(2
1waterstillinSpeed
hr/km)ba(2
1
streamofRate
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TIME AND WORK If a person can do a certain task in t hours, then in 1 hour he would
do 1/t portion of the task.
A does a particular job in a hours and B does the same job in b
hours, together they will take hours
A does a particular job in a hours more than A and B combined
whereas B does the same job in b hours more than A and B
combined, then together they will take hours to finish the job.
A does a particular job in a hours, B does the same job in b hours
and C does the same job in c hours, then together they will take
hours.
If A does a particular job in a hours and A&B together do the job in t
hours, the B alone will take hours.
ba
ab
ab
cabcababc
ta
at
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TIME ANDWORK
IfA does a particular job in a hours, B does the same job in b hoursand ABC together do the job in t hours, then
C alone can do it in hours
A and C together can do it in hours
B and C together can do it in hours
If the objective is to fill the tank, then the Inlet pipesdo positive work
whereas the Outlet pipesdo negative work. If the objective is to empty
the tank, then the Outlet pipesdo positive work whereas the InletPipesdo negative work.
btatab
abt
tb
bt
ta
at
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PIPES AND CISTERN
A pipe connected with a tank or a cistern or a reservoir, that fits it is
known as a inlet.
Outlet- A pipe connected with a tank or cistern or reservoir, emptying it
is known as a outlet
If a pipe can fill a tank in y hours then part filled in 1 hour = 1/yIf a pipe can empty a tank in y hours, then part emptied in 1 hour = 1/y
If a pipe can fill a tank in x hours and another pipe can empty the full
tank in y hours where(x>y) then on opening both the pipes the net part
filled in one hour is = ( 1/x - 1/y)
if a pipe can fill a tank in x hours and another pipe can empty the full
tank in y hours(y>x) then on opening both the pipes, the net part
emptied in 1 hour = (1/y1/x)
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PERMUTATIONS AND COMBINATIONS
When two tasks are performed in succession, i.e., they are
connected by an 'AND', to find the total number of ways ofperforming the two tasks, you have to MULTIPLYthe individual
number of ways. When only one of the two tasks is performed, i.e.
the tasks are connected by an 'OR', to find the total number of ways
of performing the two tasks you have to ADDthe individual number
of ways.
Linear arrangement of r out of 'n' distinct items (nPr):
The first item in the line can be selected in 'n' ways AND the second
in (n 1) ways AND the third in (n 2) ways AND so on. So, thetotal number of ways of arranging 'r' items out of 'n' is
(n)(n - 1)(n 2)...(n - r + 1) =)!rn(
!n
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PERMUTATIONS AND COMBINATIONS
Circular arrangement of 'n' distinct items: Fix the first item andthen arrange all the other items linearly with respect to the first item.
This can be done in (n 1)!ways.
In a necklace, it can be done in ways
Selection of r items out of 'n' distinct items (nCr):Arrange of ritems out of n = Select r items out of n and then arrange
those r items on r linear positions.
nPr=nCrx r!
Number of ways of arranging 'n' items out of which `p' are alike, 'q'
are alike, 'r' are alike in a line is given by =
2
)1n(
)!rn(!r
!n
!r!q!p
!n
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18/20
PROBABILITY
If the probability of an event occurring is P, then
the probability of that event occurring r times in
n trials is = nCrx Prx (1-P)n-r
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CONDITIONAL PROBABILITY FORMULA
conditional probability that A occurs given that B
has occurred is written as P(A|B) and defined by
P(A|B) = P(A B) / P(B)
OUTCOMESTOTAL
OUTCOMESFAVOURABLEYPROBABILITLTHEORITICA
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PROBABILITYOdds
outcomesfavorabletheofNumber
outcomefavourablenotagainstOdds
outcomesfavorablenotofnumberoutcomesfavorableofNumberfactorinOdds
If A and B are two independent events, then,
P (A B) = P (A) P (B) orP (AB) = P (A) P (B)
If the probabilities of happening of n independent events be p1, p2pnrespectively, then
(i) Probability of happening none of them
=(1p1) (1p2) . (1 - pn)(ii) Probability of happening atleast one of them
=1 - (1p1) (1p2) . (1 - pn)
(iii) Probability of happening of first event and not happening of
the remaining
= p1
(1p2
) (1p3
) (1 - pn
)
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MENSURATION
NAME OF PLANE
FIGURE
AREA IN SQUARE
UNIT
PERIMETER IN UNITS
CIRCLE r2 2r
RECTANGLE LENGTH* WIDTH 2(LENGTH+WIDTH)
SQUARE SIDE*SIDE 4*SIDE
TRIANGLE 0.5*BASE*HEIGHT SUM OF ALL SIDES
RHOMBUS LENGTH*HEIGHT 4*LENGTH OF A SIDE
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