Short cut+arithmetic+techniques+

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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 Less then {5 < 10} Is not less then { 10} Is less than or equal to { x X

}

> 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

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Pi 1,2,3...n [,\,] Constant /

x,y,z Variable /

2x x + x

=

a+bx+c Expression [a , bx,c Term]

|x| [x] Absolute Value ( ) Negative Positive

Square Root , =2, =3

Cube Root , =3, =4

n Root n

x 1/n

X y

=

Summation ,X n

,*( )+- Bracket

Logarithmsa x ( n= ) [ + , ] 10

n! n Factorial n n (n-1) (n-2)1 [ 5!=54321] npr Permutation [ n npr ,

npr= n(n-1) (n-2) (n-3) ..(n-r+1) Ex:- 6p3=654 ]

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ncr Combination / / ,ncr =

( )

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 ]

NZQR 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 / Right Angle

Measured Angle Perpendicular To Is Parallel to Therefore / Hence Since / Because / Triangle Rectangle/Square Circle

2 (Unit) () 3 (Digits) / 3 Ex:- 318 3+1+8=12 , 4 (Unit) (tens) 4 Ex:- 544 , 4 44 4

5 (Unit) () 5 6 3 2 8 (Unit) , (tens) (Hundredth) 8 Ex:- 77 264 , 264 8 , 77264 8

9 (Digits) / 9 Ex:- 288 2+8+8=18 , 9 , 288 9

(Unit) () 2, 5, 10 (oo ) , 4, 25, 100 (000) , 8, 125, 1000

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Digit () 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

Number () 87654321 8(Crores) 7(Nijut) 6(lacs) 5(Ajut) 4(Thousands) 3(Hundreds) 2(Tens) 1(Units) 4321=41000+3100+210+1

Integers ( n { -n.-5,-4,-3,-2,-1, 0, +1,+2,+3,+4,+..+n} ) Even Numbers ( 2 {0, 2, 4, 6, 8,.2n} ) Odd Number ( ) 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..)

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Consecutive Integers ( )

{ n,n+1,n+2,n+3,.} Prime Numbers ( ) ( even prime number) (Odd Prime number) 1 100 25 1060 1 200 46 1 500 95 1 1000 168 ( 2 ,3 3 , )

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) Composite Number ( ) /

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Fraction ()

Fraction ()= ( ) ()

( , x y )

Rules of fractions

+ =

- =

+ =

=

+

- =

=

-

=

= =

Continued Proportion ( ):-

=

a c = b2

Proper fraction ( ):-

> ( Ex:- ,

)

Improper fraction ( ):-

< ( Ex:- ,

)

Rational Number ( ):- - , - (0,1,2,3.n ), ()-16 , ( a/b - a b ) , -

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Irrational Number ( ): a/b - a b ) ,

( ) , ( ) ,

, ,

, , e Ex:- , , , , ,

Roman Numeral ( ):- I1, V5, X10, L50, C100, O500, M1000

Fators ( ):- , , 20 =5221 Multiples ():- , Ex:- 35/5=7 , 35/7=5 5 7 35 35 7 5

Common Factor ( ):- ,

Co-prime Number ( ) :- ,

Lowest Common Multiple L.C.M ( .. ): -

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Highest Common Factor H.C.F ( .. ):-

..

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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) 6 16 6 6 =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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(Simplification) :- BODMAS [{(Braket)}]of / Division() Multiplication () Addition (+) Subtraction(-)

a b ?

=x , x-a =b-x => x=

Formula:-- =

1008 (Divisors) ?

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\63 3\21 7

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, n Let the Numbers =x and (x+1) According to the Question, (x+1)2 x2 = n x

Formula:-- = , = +

n a , b , c d ? Formula:--

= ( a , b , c d) ..

n a , b , c d ? Formula:--

= ( a , b , c d) .. + ( ) a , b , c d n / Formula:--

= ( a , b , c d) .. + / n .. L .. ? Formula:--

= .. .. a:b .. L .. ? Formula:--

.. = ..

.. .. ?

Formula:--

.. =

.. =

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(a) 2 (b) 3 (n) 10 ? Formula:--

(a) 2 (b) 3 = 6 1 = 6 10 =(610) Formula:-- = ..

=

=

M A N B , ? Formula:--

M A , M = M A [ A =

]

N B , N = N B

= M + N

= AM +BN

=

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Varies as / is Proportional -

( , , , )

, = = , = a, b, c ,

a:b =b:c

s a:b:c a+b+c

= S ()

a = S

a:b =x:y b:c =l:m a:b:c =? a:b = x:y = (xl): (yl) = xl : yl b:c =l:m = (ly): (my)= yl : my a:b:c = xl : yl : my

n . a : b : c ? Formula:-- = a + b + c

= n ( )

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7 : 3 8 ? Formula:- Required Amount: =

Required ratio

Water =

3 =6

30 7 : 3 3 : 7 (3 into 7) 7 : 5 Formula:-- = 7 + 3 = 10

30 = 30 ( ) ( )

= 21

30 = 30 ( ) ( )

= 9

, = 3 : 7 x 3 : 7 21 : (9 + x) = 3 : 7 x = 40 7 : 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% ) Find the number whose P % (75% ) is N (90) ? Number N (90) is P % (75% ) of What number?

Formula:-- Let the Number be = x

X P% = N

X 75% = 90

What Percentage % is R(90) of N(120)?

N X% =R

120 x% =90

: 100 100

, 100

,

, 100

X% (25%) ? Formula:--

25% = (100 + 25 ) = 125

125 = 100

,, 100 ,, ,, ,, =

= 80

= ( 00 80)% =20%

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Formula:-

[ % =

]

[ % =

]]

(Increase ) + (Decrease )

+ 25% 20%

+33.33% 25%

, % %

25% , %

25% % , 25%

10(O) 20(N) ? , : 1(O) : 2(N) , ? Formula:-

% Change =

100%

Result + Increase

Result Decrease

=

100% =100% [ ]

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5% 1000 () , 5 ? Formula:-- 5% , 100 + 5 =105 100 = 105

,, 1000 ,, ,, ,, =

= 1050

5 = 1050 1000 = 50

1 ,, ,, ,, = 50/5 = 10

Formula:-

= 10

20% (x%) 10% (y%) , ? Solution: = 100x = 100y

= = 10000 xy

20% = (100+20)x =120x

10% = (100-10) = 90y

= 120x 90y = 10800xy

= 10800xy 10000xy = 800xy

10000xy = 800xy

,, ,, 100 ,, ,, ,, =

=8%

Formula:-

(C%) = x + y +

x First Value ( ) % y Second Value ( ) % , / (Increase) + / (Decrease) (Answer) + , (Answer) ,

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5% (x%) , ? Formula:-- +

C% = (+5) + (+5) + ( ) ( )

10 % (x%) , ? Formula:-- , F = S = 10

C% = (10) + (10) + ( ) ( )

5% (x%) ? Formula:-- , F = S = 5 , +

C% = (+5) + (+5) + ( ) ( )

25% , ( ) 5% ? F= + 25%

S = 5%

C% = (+25) + (5) + ( ) ( )

20% , 20% ?

C% = (-20) + (+20) + ( ) ( )

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100 20% 2002 ?

C% = (+20) + (+20) + ( ) ( )

10% 20% %

C% = (+10) + (+20) + ( ) ( )

x% (voter , worker & Student) y % , % voter , worker & Student ?

Formula:- Mix % =

f% , s% t% n ? Formula:- - Rest (n) = 100x (f% + s% + t% )x n x% a/b ? Formula:- -pass = n x% (a/b)

, , 70% 80% 10% , 360 ? Formula:-- = (100 70 10)% = 20% = (100 80 10)% = 10% = (20 + 10 + 10)% = 40% = (100 40)% = 60%

60 , = 100

,, ,, 360 ,, ,, ,, ,, ,, ,, =

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200 70% ,60% 40% 1:- ? 2:- ? Formula:-- = (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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9(M1) 3 (D1) 9(D2) ? , 9(M1) 12(D1) , 3(M1) ? Formula:- M1 D1 = M2 D2 1) M2 =

2) D2 =

500 20 5 100 ? Solution : 100 =(500 100) = 400 5 , 500 = (20 5) 15

1 ,, ,, ,, ,, ,, = (15 500)

400 ,, ,, ,, ,, ,, = ( )

[ 500 , , ]

X m , Y n X Y ? Formula:-- X m = 1

1 ,, ,, =

Y 1 =

X Y 1 = ( + ) =

= 1

,, 1 ,, ,, ,, =

Formula:-

T =

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X m , X Y C Y ?

Formula:- T =

X , Y Z a , b c ? Formula:-

T =

m n ( m n ) ? Formula:-

T =

, m n ? Formula:-

T =

[ ] X , Y Z 20 (a) , 24 (b) 30(c) ) ? Solution

X 20 = 1

X 1 =

Y 1 =

Z 1 =

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 ,, ,, =

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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3( M1) 5( W1) 20(T1) , 4( M2) 10( W2) ( T2) ? Formula:-- 3 20 = 1

3 ,, ,, 1 ,, ,, =

1 ,, ,, 1 ,, ,, =

4 ,, ,, 1 ,, ,, =

=

[ ,

, ] , 5 20 = 1

1 ,, ,, 1 ,, ,, =

10 ,, ,, 1 ,, ,, =

=

4 10 , 1 = (

+

) =

= 1

1 ,, ,, ,, = 6

Formula :

T2 =

( ) ( )

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10(L) 1(t) 50(U) 25(D) , ? Formula:-

T = ( )

t

U = Up , D = Down

T = ( ) ( )

1= 77Min

, ,

n

?

Formula:-- ( ) n = 1 (

)

=

=

= +

=

, U V [ U > V ]

,

(Relative Speed) = U +V

,

(Relative Speed) = U V

/ / X T

T X

,, 1 ,, ,, ,, =

=

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Lp ( , , ) Lt T

T =( Lp + Lt)

,, 1 ,, ,, ,, = ( )

= ( )

45( ) 100( ) 60(T) ? Formula:-- , 1 (60 60) = 45 = (45 1000)

60 ,, ,, =

750

60 ,

= +

750 = + 100 = 650 Formula:-

= ( )

45

= ( )

[ T C nver S eed in km/hr to m/sec multiply speed by

]

=650

121 ( x) 99 ( ) 40 ( ) 32 ( ) ? Formula:-

T =

, (Relative Speed) =

, (Relative Speed) =

T = ( )

= 11 Second [1 km/hr = meter/second ]

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150 ( ) 68( ) / , 8 ( ) / ? Formula:-

T =

= 0

T = ( )

= 9 Second [1 km/hr = meter/second ]

20 ( ) 30 ( ) , ? Formula:-

T =

T = 0 0 0

P (Principal / Capital / Sum )[ Invested]

I / / ( Interest / Extra money for Interest) [ ]

N / [ Per-annum ]

R (Rate of Interest) [ , 100 1 ]

A /-/ (Amount/ Interest-principal/Increased Principal)

= + P t = p t 1

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(Simple Interest)

P r % n ? r , 100 1 r

1 1

P 1

P t n

I =

I = npr [r = r% = r/100]

=

[ ] A = P + I

A = P + nPr = P (1 + nr)

= ( )

[ , , ]

C = p ( )

-

= ( )

( ) - = ( )

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(r=?) 700 (P) 5(t) 105(I) ? Solution-

700 5 = 105

100 ,, 1 ,, ,, =

Formula:-

I =

105 =

r =

5 - ? Formula:-- , X 5 - = 2X = - = 2X X = X

X 5 = X

100 ,, 1 ,, ,, =

= 20 = 20%

Formula:-

( ) =

=

r =20%

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8% (r1) [ ] 10% (r2) 5(t) 200 (I) (p=?) ? Formula:-- 100 1 = (10 8 ) = 2 100 ,, ,,, ,, 5 ,, ,, ,, = (5 2 ) = 10

10 = 100

,, 200 ,, ,, ,, =

Formula:- I =

200 =

p =2000

5 (r) 10 (t) 5000 (A) (p=?)? Formula:-- 5% , 100 10 = ( 5 10) = 50

100 10 = ( 100 + 50 ) = 150

150 = 100

,, 5000 ,, ,, ,, =

Formula:-

P = ( )

P =

( )

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300 ( ) 4 ( ) 500 ( ) 5 ( ) 148 (I) , (r=?) ? Formula:-- 300 4 = 1200 1 500 5 = 2500 1 (1200 + 2500 ) = 3700 1

3700 1 148

100 ,, ,, 1 ,, ,, =

= x % = x/100

, I1 =

, I2 =

, I1 + I2 =148

+

= 148

x = 4%

Formula:-

I = ( )

r =

r =

( 00 ) ( 00 )= 4%

10%(r% ) 600 (p) / 2 (n ) ? 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 ,

=

6 (n) 5 (n-1) ? Furmula: 1

(Profit %) = ( )

Profit % =

%

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9 (n) 10 (n + 1) ? Furmula: 1

(Loss %) =

( )

loss % =

9 (n) 11 (n+2) , 10 (n+1) ? Furmula:

(n) , (n+1) (n+2) ,

, ?

(loss) =

( , / -)

loss % =

( )

12(n) 25%(F%) 50%(S%) ? Formula:- =n , First Value=F%, Second Value=S%

= n

[ + , ]

= 12

5(m) 2(n) 35(s) 40%(P%) ?

Formula:- = ( ) ( )

=

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150(S) 20(L/P) ? Solution = (150 + 20 ) =170 170 = 20

,, 100 ,, ,, ,, =

Formula:- = + [ = ]

=

Cost = 150 +20 =170 % =

900 (S) 20% (p%) ? 900 (S) 20% (p%) ?

Formula:- =

Cost =

900 (S) , 20% (L%) , ?

Formula:- = ( ) ( )

Cost =

1200(n) 15%(p%) , 5%(L%) ? Solution: 100 , 100 P% , 100 = (100 + P )

,, n ,, ,, ,, = ( )

L% , 100 = (100 - L )

( )

,, ,, ,, =

( )

( )

[ P% , L% p% 5%(L%) ]

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8% (T%) 15%(p%) 280(C) , (Marked Price) ? Formula:-- 15% , 100 = (100 +15 ) =115 ,, 280 ,, ,, ,, =

= 322

8% ,

(100 - 8 ) 92 = 100

,, 322 ,, ,, ,, ,, = = 350

30(n) 55(C) 20%(n 20% ) 40(S) 12 ? Formula : ( ) = 30 30 20% =24

(Profit) =(

)

Profit = (

0)

25%(R% -reduction) 120(T) 30(n) ? Formula:-

= R% (

)

Cost=

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10%(L%) 40(C) , 20%(p%) ? Solution %

10% = (100 10) = 90 20% = (100 + 20 ) = 120 (120 90) = 30 30 100

,, ,, 40 ,, ,, ,, ,,

Formula:-

=

40 10% 20% ,

10% + 20% =40

15% = 40

1% =

100% =

Formula:-

=

=

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10%(L%) 20%(C%) 50 , 40% (P%) ? Solution: 3 % 20% = (100 20) = 80 40% = (100 + 40 ) = 140 40% 100 = 140

,, 80 ,, ,, ,,

= 112

10% , = (100 10 ) =90 = (112 -90) = 22

22 = 100

,, 50 ,, ,, ,, =

Formula:

10% , Sells1 = (100 10) = 90

20% = (100 20 ) = 80 ,

profit , 80 40% =32

,Sells2 = + = 80 + 32 = 112

=

[ Absolute Value Negative Positive

]

Cost =

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4 (X) 5 (n) , 5(Y) 4 (m) ? Solution

5 = 4 1 ,, ,, =

, 4 = 5 1 ,, ,, =

= - = =

[ ]

=

,, ,, 100 ,, ,, ,, =

Formula

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X Y ? 5 , 4 ? Splution: X = 1

1 ,, ,, =

Y = 1 1 ,, ,, =

= =

=

,, ,, 100 ,, ,, ,, = ( )

Formula

= ( )

= ( )

International Counting System ( ): - 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) Measurement And Unit ( )

S.I International Systems of Units 1960 CGS Centimeter . Gram .Second M.K.S Meter . Kilogram . Second F.P.S Foot .Pound .Second Local system( )

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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 kilogram= 2.2 (lbs) pounds 1 Seer = .93 kg 1 mound = 40 seer = 37.2 kg 1 quintal = 100 kg 1 ton = 1000 kg

1 m_t_r = 100 C_ntim_t_r = 39.37 In]hs = 3.28 `__t = 1.0936 Y[r^s = 0.00062 mil_s 1 kilogram = 1000 grams = 2.2 pounds = 35.27 Ounces = 0.157 Stone(uk) 1 meter 2 = 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

30(T) 20(F) 15(S) ? Formula : Total Number = First Individual group + Second Individual group (Common Group) F S F + S ( F S)

F S =

F S =

30 = 20 + 15 (F S )

(F S )

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1 12 12 = 3600

,, ,, ,, ,,

= 0

N = n 0

1 0 ( )

H M = ( ) ( )

HM =

[ () ]

0 / 0

Examples:

4 5 ( ) ( )

=

2 50 ( ) ( )

= [ > 0 ]

= 0

3 ( ) ( )

= 0

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Short cut+arithmetic+techniques+