ShortCut Arithmetic Techniques(Update) by Tanbircox
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Menu Bar View Auto /Automatically Scroll
( )
pdf Options View Go To (
Adobe Reader Foxit Reader ), Page number
; OK
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+
Plus / add [ Sum / Total]
Minus / Subtract /Deduct [ Difference]
Times / Into/ dot /of /Multiply [Product / Multiplication ]
, /,
Division , Divisible , Remainder
a(dividend-) b(Divisor-)= c(Quotient-)
Plus or Minus
=
Equal / Is Approximately Equal
Is not Equal
Is greater then {5> 2}
Is not greater then {5
20}
Is greater than or equal to ( / )
% Percentage( 100 )
Infinity /
Varies as / is Proportional
Implies/or
If and only if
Pi
1,2,3...n
[ \ ]
Constant/
x y z
Variable /
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2x
x + x
=
a
+bx+c
Expression [a,bx,c Term]0
n0 =n , n0 =0 , 0/n =0 , n/o = (anything 0) = Undefined ()
|x|
[x] Absolute Value ( ) Negative Positive
Square Root , =2, =3
Cube Root , =3, =4
n Rootn x 1/n
X y
=
Summation ,X n
*
+- Bracket
Logarithmsa x( n= )[+ , ]
10 n
n Factorialn n (n-1) (n-2)1 [ 5!=54321]
n
p
r
Permutation [ n npr ,
npr= n(n-1) (n-2) (n-3) ..(n-r+1) Ex:-6p3=654 ]
n
c
r
Combination/ /,ncr=
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A=
*
,
,
,
+
A , a,b,c,d
Intersection /cap [/
] [AB={x:xA xB}]
Union/cup [
]=> ( ) [AB={x:xA xB}]
Element of / Belongs to / [Ex: bA]
Is not an Element of/not Belongs to
/ Subset of [A / B / ]
/
Superset
Empty Set
A\B
[B A , A /
A ] A-B={x:xA xB}A
Complementary set [U\A=U-A={xU : xA }
P(A)
Power Set [A n P(A)
2n]
N
Z
Q
R
N( / +n),Z( +n,0,+n)
Q
(0,+n, ),
R( ), ( ) Q=R-Q
Straight line ( )
Ray ( )
Line Segment ( )
Similar to
Almost Equal to
Is Equivalent to/ Congruent
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Angle
/RightAngle
Measured Angle
Perpendicular To
Is Parallel to
Therefore / Hence
Since / Because /
Triangle
Rectangle/Square
Circle
(Unit) ()
3
(Digits) / 3
Ex:- 3183+1+8=12 ,
(Unit) (tens) 4
Ex:- 544 , 4 44 4
(Unit) () 5
3 2
(Unit), (tens) (Hundredth)
8 Ex:- 77 264 , 2648 , 772648
(Digits) / 9
Ex:- 2882+8+8=18 , 9 , 2889
(Unit) () 2, 5, 10
(oo) , 4, 25, 100
(000) , 8, 125, 1000
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0,1,2,3,4,5,6,7,8,9
1 100
0 11
2 9 (2,3,4,5,6,7,8,9) 20
1 21
87654321
8(Crores) 7(Nijut) 6(lacs) 5(Ajut) 4(Thousands) 3
(Hundreds) 2(Tens) 1(Units)
4321=41000+3100+210+1
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{
-n.-5,-4,-3,-2,-1, 0, +1,+2,+3,+4,+..+n}
2 {0,2,4,6,8,.2n}
2 {1,3,5,7,9.(2n+1)}
Even Even=Even , Odd Odd=Odd , Even Odd=Even
Even + Even=Even , Odd + Odd=Even , Even Odd=Odd
Even / Even=Even , Even /Odd=Odd , Odd/Even=Odd
Odd Odd =Odd , Odd Even=Odd , Even Even=Even , Even Odd=Even
(2,4,6.) (3,5,7..)
{ n,n+1,n+2,n+3,.}
( even prime
number)
(Odd Prime number)
1 100 25 1060
1 200 46 1 500 95
1 1000 168
( 2 ,3
3 , )
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1 100
1-10 2,3,5,7 4
11-20 11,13,17,19 4
21-30 23,29 2
31-40 31,37 2
41-50 41,43,47 3
51-60 53,59 2
61-70 61,67 2
71-80 71,73,79 3
81-90 83,87 2
91-100 97 1
(4422322321)
(1232232244)
/
Fraction ()=
, x y )
, = Rules of fractions
+
=
- =
+
=
=
+
-
=
=
-
=
=
=
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=
a c = b
2
> ( Ex:- , )
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,
, , , , , , ,
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- , -(0,1,2,3.n ), ()-16 , ( a/b
- a b ) , -
a/b - a b ) ,
( ) , ( ) , , , , , e Ex:- , , , , ,
I1, V5, X10, L50, C100, O500, M1000
Greek Alphabet
Alpha Beta Gamma Delta
Epsilon Zeta Eta
Theta Iota Kappa Lambda Mu Nu Xi Omicron
Pi Rho Sigma Tau Upsilon Phi Kai Psi
Omega
,
,
20 =5221
,
Ex:- 35/5=7 , 35/7=5 5 7 35 35 7 5
,
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,
-
..
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2304 (Square Root )
74 28
1)
2) ,
3) 74 64, = 8:4) 8 74 64
5)
74 64
10 28
1028 ( )
6) 8 82= 16 ( )
7) 16
1028 1028
8) 616 66=996 7 ( 16 7 7= 1169) 1028
9) 1028 996 32 862 = 172
32
10)
, 86
11) 74 28 32 7396
86
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BODMAS
[{(Braket)}]of / Division() Multiplication ()
Addition (+) Subtraction(-)
=x , x-a =b-x => x= Formula:-- =
1008 = 2222337=243271
= (4+1)(2+1)(1+1)=30
Formula:-- x =ambncl
=(m+1)(n+1)(l+1)
2\1008
2\504
2\252
2\126
3\633\21
7
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n
Let the Numbers =x and (x+1)
According to the Question, (x+1)2x2= n x
= , = +
= ( a , b , c d) ..
= ( a , b , c d) ..
+
= ( a , b , c d) .. + /
= .. ..
.. = ..
.. =
.. =
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Varies as
/ is Proportional
-
,,,
, =
= , =
a, b, c ,
a:b =b:c
a+b+c = S ()
a = S
a:b = x:y = (xl): (yl) = xl : ylb:c =l:m = (ly): (my)= yl : my
a:b:c = xl : yl : my
Formula:-- = a + b + c
= n
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Formula:-
Required Amount: = Required ratio
Water =
3 =6
Formula:--
= 7 + 3 = 10
30 = 30
( ) = 21
30 = 30 ( )
= 9
, =
3 : 7
x 3 : 7
21 :(9 + x) = 3 : 7x = 407 : 5
10 = 30
0/0 3
= 7 : (3+2) = 7 :5 1 = 3
6
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100 (100)
x % = N (90) P % (75% )
Formula:--Let the Number be = x
X P% = NX 75% = 90What Percentage % is R(90) of N(120)?
N X% =R
120 x% =90
100
100
,100
,
, 100
-
25% = (100 + 25 ) = 125
125 = 100
,, 100 ,, ,, ,, = = 80
= 00 80)%=20
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Formula:-
[ % =
]
[ % =
]]
(Increase ) + (Decrease )
, % %
25% , %
25% % , 25%
Formula:-
% Change =
100%
Result + Increase
Result Decrease = 0 00 100% =100% [ ]
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Formula:--5% , 100 + 5 =105
100 = 105
,, 1000 ,, ,, ,, =
= 1050
5 = 1050 1000 = 501 ,, ,, ,, = 50/5 = 10
Formula:-
= 10
Solution:= 100x = 100y
= = 10000 xy20% = (100+20)x =120x
10% = (100-10) = 9
0y
= 120x 90y = 10800xy = 10800xy 10000xy = 800xy 10000xy = 800xy
,, ,, 100 ,, ,, ,, =
=8% Formula:-
x First Value ( ) % y Second Value ( ) % ,
/ (Increase) + / (Decrease) (Answer) + ,
(Answer) ,
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Formula:--
+
C% = (+5) + (+5) +
Formula:--
,
F=S = 10
C% = (10) + (10) +
Formula:-- ,
F=S = 5
, +
C% = (+5) + (+5) +
F= + 25%
S =5%
C% = (+25) + (
5) +
C% = (-20) + (+20) +
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C% = (+20) + (+20) +
C% = (+10) + (+20) +
Formula:-Mix % =
Formula:-- Rest (n) = 100x (f% + s% + t% )x
Formula:--pass = n x% (a/b
)
, = 100
= (100+25 ) 125
125 =100
,, ,, 100 ,, ,, ,, ,, 80 = (100 80 ) = 20
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,
100 =25
,, 64 ,, ,, ,, ,, =
, = (6416) 48
,
40 = 100
,, 48 ,, ,, ,, ,, =
120
= (12048) 72
, = (72 16) 56
,
,
Formula:--
= (100 70 10)% = 20% = (100 80 10)% = 10% = (20 + 10 + 10)% = 40% = (100 40)% = 60% 60 , = 100
,, ,, 360 ,, ,, ,, ,, ,, ,, =
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= (60 40)% = 20% = (70 40)% = 30% = (40 + 30 + 20)% = 90%
= (100 90)% = 10%[1 10% ] 100 = 10
,, 200 ,, ,, ,, ,, ,, ,, =
, , ,
, ,
()
[ , ]
X = Y 1 = (X Y)[ , ]Z =
[ , ]
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1 1 2
,
Formula:- M1
D
1
= M
2
D
2
1)M2= 2)D2 =
Solution :
100 =(500100) = 400 5 ,500 = (20 5) 151 ,, ,, ,, ,, ,, = (15 500)
400 ,, ,, ,, ,, ,, =
00 [ 500
,
, ]
Formula:--
X m = 1 1 ,, ,, =
Y 1 = X Y 1 = (
+
) =
=1
,, 1 ,, ,, ,, = Formula:-
T =
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Formula:- T =
Formula:-
T =
Formula:-
T =
Formula:-
T =
[
]
Solution
X 20 = 1 X 1 =
Y 1 =
Z1 =
X , Y Z 1 = ( ) = 1
,, 1 ,, ,, ,, = 8
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Formula:--
1 = 1/8
,, 6 ,, ,, ,, = 6/8
= (1 ) = X 1 = 20
,, ,, ,, = (20 ) =20/4 = 5
Formula:--
X 1 = 1/ 20 5 ,, ,, =
0
X 5 X , Y Z = (1
) =
X , Y Z 1/8 = 1 ,, 1 ,, ,, ,, = 8 ,, ,, ,, ,, = = 6
= X , Y Z + X 5=6 + 5 = 11
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1 1 1 2
2 2
Formula:--
3 20 = 1
3 ,, ,, 1 ,, ,, = 0
1 ,, ,, 1 ,, ,, = 0 4 ,, ,, 1 ,, ,, = 0 = [ ,
, ],
5 20 = 1
1 ,, ,, 1 ,, ,, = 0 10 ,, ,, 1 ,, ,, = 00 =
0
410,
1 = ( +
0) =
= 1 1 ,, ,, ,, = 6Formula :
T2 =
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Formula:-
T =
t U = Up , D = Down
T = 1= 77Min
Formula:-- ( )n= 1 ( )
=
=
=
+
=
, U V [ U >V]
,
(Relative Speed)= U +V ,
(Relative Speed
)= U
V
/ / X T
T X ,, 1 ,, ,, ,, =
=
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p
Lt
T =( Lp+ Lt) ,, 1 ,, ,, ,, =
=
Formula:-- ,
1 (60 60) = 45 = (45 1000)
60 ,, ,, = 0 0 750 60 ,
= +
750 = + 100 = 650Formula:-
= 45 =
[ T Cnver Seed in km/hrto m/secmultiply speed by
]
=650x
T = , (Relative Speed)= , (Relative Speed)= T =
= 11 Second [1 km/hr = meter/second ]
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Formula:-
T =
=0T = 0 0 = 9 Second [1 km/hr =
meter/second ]
Formula:-
T = T = 0 0 0
(Principal / Capital / Sum )[ Invested]
/ / ( Interest / Extra money for Interest) [ ]
/ [ Per-annum ]
(Rate of Interest) [ , 100 1 ]
/-/ (Amount/ Interest-principal/Increased Principal)
= +
P t = p t 1
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r
,100 1 r
1 1 P 1
P tn
I = I = npr [r = r% = r/100]
[
]
A =P + I
A = P + nPr = P (1 + nr)
P =
[r = r% = r/100]
P =
[ ,, ]
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P r
n C = p
= (C) (P)= P P
=
=
Solution-
7005 = 105
100 ,, 1 ,, ,, =
Formula:-
I =
105=
r =
, X5 - = 2X
= - = 2X X = X
X 5 = X
100 ,, 1 ,, ,, = = 20 = 20%
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Formula:-
( ) =
=
r 0
1 2
Formula:--
100 1 =(10 8 ) = 2100,, ,,, ,, 5 ,, ,, ,, = (5 2 ) = 10 10 = 100
,, 200 ,, ,, ,, = 00 000 Formula:- I =
200 = p =2000
Formula:--
5% , 100 10
= ( 5 10) = 50
100 10 = ( 100 + 50 ) = 150 150 = 100
,, 5000 ,, ,, ,, = 00 0000 Formula:-
P =
P =
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Formula:--
300 4 = 1200 1
500 5 = 2500 1
(1200 + 2500 ) = 3700 1 3700 1 148
100 ,, ,, 1 ,, ,, = 0000 = x % = x/100
, I1=00
00
, I2= 00 00
, I1 + I2 =148
00 00 + 00 00 = 148x = 4%Formula:-
I = r= r = 00 00 00= 4%
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+ 5 = 500
+ 5 = 460
[ ]
2 = 40 1 ~ ~ = = 203 ~ ~ = 203 = 60
= (46060) = 400
400 1 20
1 ~ 1 ~ ~ 20/400
100 ~ 1 ~ ~20
400 00
Formula:-
C = p
C = 600
C = 726
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(Cost Price ) CP :-
/
(Selling Price )SP:-
(Profit) = (SP)-
(CP)/(Profit /Gain) P:-
(loss)= (CP) - (SP)/ (Loss)L:-
,
-
X % x %
x
C x % ,
=
X% c = ( C + )
X % C = ( C )
C P ,
=
Furmula: 1
(Profit %)= 00
Profit % = 00 %
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Furmula: 1
(Loss %)=
loss % = 00
0
Furmula:
(n) , (n+1) (n+2) ,
, ?
(loss) = /-
loss % = 000
Formula:- =n , First Value=F%
, Second Value=S%
= n [ + , ]
= 12
Formula:- =
= 00 00 0
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Solution = (150 + 20 ) =170 170 = 20
,, 100 ,, ,, ,, = 0 000 Formula:-
=
+ [ =
]
=
Cost = 150 +20 =170 % =0 000
Formula:-
=
Cost = 00 0000 0
Formula:- =
Cost = 00 0000 0
Solution: 100 , 100 P%,
100 = (100 + P )
,, n ,, ,, ,, = 0000 L%,
100 = (100 -L )
0000 ,, ,, ,, = 00 00 0000 [ P% ,L% p% 5%(L%)
]
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Formula:--
15%,
100 = (100 +15 ) =115
,, 280 ,, ,, ,, = = 3228% ,
(100 -8 ) 92 = 100
,, 322 ,, ,, ,, ,, = = 350
Formula : ( )= 30 30 20
% =24
(Profit)=(
Profit = 0
Formula:-
= R% ( )
Cost= 00 00
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Solution %
10% = (100 10) = 9020% = (100 + 20 ) = 120
(120 90) = 30 30100
,, ,, 40 ,, ,, ,, ,, Formula:-
=
40 10% 20%
,
10% + 20% =4015% = 401% = 0
100% = 0 00 Formula:-
=
= 00 0 0
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Solution: 3 %
20% = (100 20) = 8040% = (100 + 40 ) = 140
40% 100 = 140
,, 80 ,, ,, ,, 0 000 = 11210% , = (100 10 )=90
= (112 -90) = 22
22= 100,, 50 ,, ,, ,, =
00 0
Formula:
10% , Sells1= (100 10)
= 90
20% = (100 20 ) = 80 ,
profit , 80 40% =32
,Sells2 = + = 80 + 32 = 112
=
[ Absolute Value Negative Positive]
Cost = 00 0
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Solution:
5 = 4
1 ,, ,, = ,
4 = 5 1 ,, ,, = = - =
=
0
[ ]
=
0
,, ,, 100 ,, ,, ,, =
Formula
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Solution:
X = 1
1 ,, ,, =
Y = 11 ,, ,, = = =
=
,, ,, 100 ,, ,, ,, = 00
Formula
=
= 00
Solution:
= (380+20)400 400 =20
,, 100 ,, ,, ,,
Solution:
10% = (100-10) 90
5% = (100+5) 105
= (10590) 15 15 100
,, 45 ,, ,, ,, ,, 300
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Solution:
20% = (100+20) 120
10% = (100-10) 90
20% , 100 = 120
,, 90 ,, ,, ,, = =108
% , = (100
)
= (100 ) 31
2 =100
,, 31 ,, ,, ,, ,, = 200
Solution:
x % , = 00 ( 0 0 ) = 100 ,, n ,, ,, ,, = y % , = 00 100 = ( 0 0 ) ,, ,, ,, ,,=
= n
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Solution:
36 =12
100 ,, ,, ,,
20% , 100 = (100 + 20) 120
20% ,
= 120
20 ,, ,, ,,
Solution:
15% 1200 + 1200 15% (1200 15100
)1200+180 = 1380
5% 1380 1380 5%
1380 69 = 1311
Solution:
5 = 2
100 ,, ,, = 4040% ,100 (100+40) 140
140 =40
35 ,, ,, ,, ,, = 10
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Solution:
12=20
1 ,, ,, ,, = 53
1 = = 2
5
3 =
1
3
53 = 1
3
,, 100 ,, ,, 20 [ ]
Solution:
3 = 1
1 ,, ,, ,, =
2 = 1
1 ,, ,, ,, = 2
1 = = 1
2 1
3 =
16
[ ] 1
3 = 1
6
,, 100 ,, ,, 50
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Solution:
, 5 = x
1 ,, ,, ,, =
4 = x
1 ,, ,, ,, =
1 = =
=
=
,, 100 ,, ,, 25
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1 Lac = 105
1 Million = 106= 10 lac
1 Crore =107=10 million
1 Billion = 109 (USA) =1012(Eu)
1 Trillion = 1012(USA) = 1018(Eu)
1 kilogram= 2.2 (lbs) pounds
1 Seer = .93 kg
1 mound = 40 seer = 37.2 kg
1 quintal = 100 kg
1 ton = 1000 kg
S.IInternational Systems of Units 1960
CGSCentimeter . Gram .Second
M.K.SMeter . Kilogram . Second
F.P.SFoot .Pound .Second
12 Inch = 1 foot , 3 foot = 1 Yard , 1760 Yard = 1 mile
Relationship
Distance Area Volume
1 Inch = 2.54 Centimeter 1 Inchs2= 6.45 cm2 1 liter = 1000 Cubic Centimeter
1 Meter = 39.37 Inch 1 Hectare = 10000 meter2 1 Cubic meter = 1000 liters
1 mile = 1.61 kilometer 1 Katha = 720 feet2 1 Cubic foot = 28.31 liters
1 Nautical Mile = 1.853km 1 Acre = 4047 meter2 1 gallon = 3.78 liters(us) = 4.54 liters(uk)
1 km2 = 247 Acres 1 Cubic Centimeter= 1 gram
1 m_t_r = 100 C_ntim_t_r = 39.37 In]hs = 3.28 `__t = 1.0936 Yr^s = 0.00062 mil_s
1 kilogram = 1000 grams = 2.2 pounds = 35.27 Ounces = 0.157 Stone(uk)
1 meter2= 10.76 feet2=1550 Inchs2= 10000 centimeter2
1 Square kilometer = .3861 mile2= 100 hectares = 247 acres
1 mile2= 2.589 kilometers2= 259 hectare = 640 acres
1 Celsius = 33.8 Fahrenheit = 274.15 kelvin
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F S F + S F S F S= F S= 30 = 20 + 15 F S F S
1 12
12 = 3600 ,, ,, ,, ,, = 0N = n
0
1 0
H M = ()() HM = [ () ]
0 / 0
Examples: = = [>0]
= 0
=
0
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:
()
()(x )
x
()
()
()x
:
,A= q n
, q = n =
(
,, W = q x n
, q= ,
n= x=
w = nx
, d = v t.
, v = t=
,Q(t)
= Q
0
q t
, Q0=
q =
t=
Q(t) = t(+ )
P = b r
, b=
r = = = S%P== b S%
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