Short cut arithmetic techniques(update)
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গণিতের শর্টকাট ফর্মুলার (ShortCut Math Techniques) এক্সক্লুসিভ বাংলা ই-বুক ।বিসিএস,ব্যাংকার্স রিক্রুটম্যান্ট, IBA,MBA,GMATও GRE ও যে কোন প্রতিয়োগিতামূলক পরীক্ষার প্রস্ততির জন্য
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- 1. Want more Updates http://facebook.com/tanbir.ebooksfacebook
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/Automatically Scroll ( ) pdf Options View Go To ( Adobe Reader
Foxit Reader ), Page number ; OK
- 2. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.com+ Plus / add [ Sum /
Total ] Minus / Subtract /Deduct [ Difference ] Times / Into/ dot
/of /Multiply [Product / Multiplication ], /,Division , Divisible ,
Remaindera(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 Pi
1,2,3...n[,,]Constant / x,y,z Variable /
- 3. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.com2x 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, =3Cube Root , =3, =4n 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]nprPermutation [ n npr
,npr= n(n-1) (n-2) (n-3) ..(n-r+1) Ex:-6p3=654 ]ncrCombination / /
,ncr =( )
- 4. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.comA=*, , , + 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 AB[B A
, A / A ] A-B={x:xA xB}A Complementary set [UA=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
- 5. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.com Angle / Right Angle
Measured Angle Perpendicular To Is Parallel to Therefore / Hence
Since / Because / Triangle Rectangle/Square Circle (Unit) () 3
(Digits) / 3 Ex:- 318 3+1+8=12 , (Unit) (tens) 4 Ex:- 544 , 4 44 4
(Unit) () 5 3 2 (Unit) , (tens) (Hundredth) 8 Ex:- 77 264 , 264 8 ,
77264 8 (Digits) / 9 Ex:- 288 2+8+8=18 , 9 , 288 9 (Unit) () 2, 5,
10 (oo ) , 4, 25, 100 (000) , 8, 125, 1000
- 6. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.com0,1,2,3,4,5,6,7,8,9 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
- 7. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.com{ -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=EvenEven + Even=Even , Odd
+ Odd=Even , Even Odd=OddEven / Even= Even , Even /Odd=Odd ,
Odd/Even= OddOddOdd=Odd , OddEven=Odd , EvenEven=Even ,
EvenOdd=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 , )
- 8. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.com1 100 1-10 2,3,5,7
411-20 11,13,17,19 421-30 23,29 231-40 31,37 241-50 41,43,47 351-60
53,59 261-70 61,67 271-80 71,73,79 381-90 83,87 291-100 97 1
(4422322321) (1232232244) / Fraction ()=( )()( , x y ) , = Rules of
fractions + = - = + = = + - = = - = = =
- 9. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.com= a c = b2 > ( Ex:-
, ) < ( Ex:- , )
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/gmail/skype: - http://tanbircox.blogspot.com ,, , , , , , ,
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/gmail/skype: - http://tanbircox.blogspot.com- , - (0,1,2,3.n ),
()-16 , ( a/b - a b ) , - a/b - a b ) , ( ) , ( ) , , , , , e Ex:-
, , , ,,I1, V5, X10, L50, C100, O500, M1000 Greek AlphabetAlpha
Beta Gamma Delta Epsilon Zeta EtaTheta Iota Kappa Lambda Mu Nu Xi
OmicronPi Rho Sigma Tau Upsilon Phi Kai PsiOmega , , 20 =5221 ,
Ex:- 35/5=7 , 35/7=5 5 7 35 35 7 5 ,
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/gmail/skype: - http://tanbircox.blogspot.com , - ..
- 14. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.com2304 (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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- 16. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.com BODMAS[{(Braket)}]of
/ Division() Multiplication () Addition (+) Subtraction(-) =x , x-a
=b-x => x=Formula:-- = 1008 = 2222337=243271 =
(4+1)(2+1)(1+1)=30Formula:-- x =ambncl
=(m+1)(n+1)(l+1)210082504225221263633217
- 17. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.comnLet the Numbers =x
and (x+1)According to the Question, (x+1)2 x2= n x = , = + = ( a ,
b , c d) .. = ( a , b , c d) .. + = ( a , b , c d) .. + / = .. ..
.. = .. .. = .. =
- 18. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.com- (a) 2 (b) 3 = 61 = 6
10 =(610) = .. = = -M A , M = M A [ A =]N B , N = N B = M + N = AM
+BN =
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/gmail/skype: - http://tanbircox.blogspot.comVaries as / is
Proportional - ( , , , ) , = = , = a, b, c ,a:b =b:c a+b+c = S () a
= S a:b = x:y = (xl): (yl) = xl : yl b:c =l:m = (ly): (my)= yl : my
a:b:c = xl : yl : myFormula:-- = a + b + c = n ( )
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/gmail/skype: - http://tanbircox.blogspot.comFormula:-Required
Amount: = Required ratio Water = 3 =6Formula:-- = 7 + 3 = 1030 = 30
( )( )= 21 30 = 30 ( )( )= 9 , = 3 : 7 x 3 : 7 21 : (9 + x) = 3 : 7
x = 407 : 5 10 = 30 0/ 0 3 = 7 : (3+2) = 7 :5 1 = 3 6
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/gmail/skype: - http://tanbircox.blogspot.com 100 (100) x % =N (90)
P % (75% )Formula:-- Let the Number be = x X P% = N X 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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/gmail/skype: - http://tanbircox.blogspot.comFormula:- [ % = ] [ %
= ]] (Increase ) + (Decrease ) , % % 25% , % 25% % , 25% Formula:-%
Change = 100%Result + IncreaseResult Decrease =0 00 100% =100% [
]
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/gmail/skype: - http://tanbircox.blogspot.comFormula:-- 5% , 100 +
5 =105 100 = 105 ,, 1000 ,, ,, ,, = = 1050 5 = 1050 1000 = 50 1 ,,
,, ,, = 50/5 = 10 Formula:- = 10 Solution: = 100x = 100y = = 10000
xy20% = (100+20)x =120x10% = (100-10) = 90y = 120x 90y = 10800xy =
10800xy 10000xy = 800xy 10000xy = 800xy,, ,, 100 ,, ,, ,, = =8%
Formula:-x First Value ( ) % y Second Value ( ) % , / (Increase) +
/ (Decrease) (Answer) + , (Answer) ,
- 24. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.comFormula:-- + 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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/gmail/skype: - http://tanbircox.blogspot.com C% = (+20) + (+20) +(
) ( ) C% = (+10) + (+20) +( ) ( )Formula:- Mix % =Formula:- - Rest
(n) = 100x (f% + s% + t% )xFormula:- -pass = n x% (a/b) , = 100 =
(100+25 ) 125 125 =100 ,, ,, 100 ,, ,, ,, ,, 80 = (100 80 ) =
20
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/gmail/skype: - http://tanbircox.blogspot.com , 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 ,, ,, ,, ,, ,, ,, =
- 27. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.com = (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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/gmail/skype: - http://tanbircox.blogspot.com1 1 2 ,Formula:- M1 D1
= M2 D21) M2 =2) D2 =Solution :100 =(500 100) = 400 5 ,500 = (20 5)
15 1 ,, ,, ,, ,, ,, = (15 500) 400 ,, ,, ,, ,, ,, =( )00[ 500 , ,
]Formula:--X m = 1 1 ,, ,, = Y 1 = X Y 1 = ( + ) = = 1 ,, 1 ,, ,,
,, = Formula:- T =
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/gmail/skype: - http://tanbircox.blogspot.comFormula:- T =
Formula:- T =Formula:- T =Formula:- T = [ ]SolutionX 20 = 1 X 1 = Y
1 = Z 1 = X , Y Z 1 = ( ) = 1 ,, 1 ,, ,, ,, = 8
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/gmail/skype: - http://tanbircox.blogspot.comFormula:-- 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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/gmail/skype: - http://tanbircox.blogspot.com1 1 1 22 2Formula:--3
20 = 1 3 ,, ,, 1 ,, ,, =0 1 ,, ,, 1 ,, ,, =0 4 ,, ,, 1 ,, ,, =0 = [
, , ],5 20 = 1 1 ,, ,, 1 ,, ,, =0 10 ,, ,, 1 ,, ,, =00 =0 4 10 ,1 =
( +0) = = 1 1 ,, ,, ,, = 6 Formula : T2 =( ) ( )
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/gmail/skype: - http://tanbircox.blogspot.comFormula:- T =( ) t U =
Up , D = Down T =( ) ( ) 1= 77MinFormula:-- ( ) n = 1 ( ) = = = + =
, U V [ U > V ] , (Relative Speed) = U +V , (Relative Speed) = U
V / / X T T X ,, 1 ,, ,, ,, = =
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/gmail/skype: - http://tanbircox.blogspot.compLt T =( Lp + Lt) ,, 1
,, ,, ,, =( ) =( )Formula:-- ,1 (60 60) = 45 = (45 1000) 60 ,, ,,
=0 0 750 60 , = + 750 = + 100 = 650 Formula:- =( ) 45 =( )[ T C
nver S eed in km/hr to m/sec multiply speed by ] =650x T = ,
(Relative Speed) = , (Relative Speed) = T =( )= 11 Second [1 km/hr
= meter/second ]
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/gmail/skype: - http://tanbircox.blogspot.comFormula:- T = = 0 T =0
0( )= 9 Second [1 km/hr = meter/second ]Formula:- T = T =00 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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t n 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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/gmail/skype: - http://tanbircox.blogspot.com P rn C = p ( ) = (C)
(P)= P ( ) P = ( ) = ( ) Solution-700 5 = 105 100 ,, 1 ,, ,, =
Formula:- I = 105 = r = , X 5 - = 2X = - = 2X X = X X 5 = X 100 ,,
1 ,, ,, = = 20 = 20%
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/gmail/skype: - http://tanbircox.blogspot.comFormula:- ( ) = = r 01
2Formula:--100 1 = (10 8 ) = 2 100 ,, ,,, ,, 5 ,, ,, ,, = (5 2 ) =
10 10 = 100 ,, 200 ,, ,, ,, =00 000Formula:- I = 200 = p =2000
Formula:--5% , 100 10 = ( 5 10) = 50 100 10 = ( 100 + 50 ) = 150
150 = 100 ,, 5000 ,, ,, ,, =00 0000Formula:- P =( ) P =( )
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/gmail/skype: - http://tanbircox.blogspot.com)Formula:--300 4 =
1200 1 500 5 = 2500 1 (1200 + 2500 ) = 3700 1 3700 1 148 100 ,, ,,
1 ,, ,, =0000 = x % = x/100 , I1 =0000 , I2 =0000, I1 + I2
=1480000+0000= 148 x = 4%Formula:-I =( ) r = r =00( 00 ) ( 00 )=
4%
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/gmail/skype: - http://tanbircox.blogspot.com + 5 = 500 + 5 = 460 [
] 2 = 40 1 ~ ~ = = 203 ~ ~ = 203 = 60 = (46060) = 400 400 1 20 1 ~
1 ~ ~ 20/400100 ~ 1 ~ ~2040000Formula:- C = p ( ) C = 600 ( )C =
726
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/gmail/skype: - http://tanbircox.blogspot.com (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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/gmail/skype: - http://tanbircox.blogspot.comFurmula: 1 (Loss %) =(
) loss % =000Furmula:(n) , (n+1) (n+2) , , ? (loss) =( , / -) loss
% =00( 0)Formula:- =n , First Value=F%, Second Value=S% = n [ + , ]
= 12 Formula:- = ( )( ) = 0000 0
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/gmail/skype: - http://tanbircox.blogspot.comSolution = (150 + 20 )
=170 170 = 20 ,, 100 ,, ,, ,, =0 000Formula:- = + [ = ] = Cost =
150 +20 =170 % =0 000 Formula:- = Cost =00 0000 0Formula:- =( ) ( )
Cost =00 0000 0Solution: 100 , 100 P% , 100 = (100 + P ) ,, n ,, ,,
,, =( 00 )00L% , 100 = (100 - L ) ( 00 )00,, ,, ,, =( 00 )00( 00
)00[ P% , L% p% 5%(L%) ]
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/gmail/skype: - http://tanbircox.blogspot.comFormula:--15% , 100 =
(100 +15 ) =115 ,, 280 ,, ,, ,, = = 322 8% , (100 - 8 ) 92 = 100 ,,
322 ,, ,, ,, ,, = = 350 Formula : ( ) = 30 30 20% =24 (Profit) =( )
Profit = ( 0) Formula:- = R% ( ) Cost=0000
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/gmail/skype: - http://tanbircox.blogspot.comSolution % 10% = (100
10) = 90 20% = (100 + 20 ) = 120 (120 90) = 30 30 100 ,, ,, 40 ,,
,, ,, ,, Formula:- = 40 10% 20% , 10% + 20% =40 15% = 40 1% =0 100%
=0 00Formula:- = =000 0
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/gmail/skype: - http://tanbircox.blogspot.comSolution: 3 % 20% =
(100 20) = 80 40% = (100 + 40 ) = 140 40% 100 = 140 ,, 80 ,, ,, ,,0
000 = 112 10% , = (100 10 ) =90 = (112 -90) = 22 22 = 100 ,, 50 ,,
,, ,, =00 0Formula: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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/gmail/skype: - http://tanbircox.blogspot.comSolution:5 = 4 1 ,, ,,
= ,4 = 5 1 ,, ,, = = - = =0[ ] =0 ,, ,, 100 ,, ,, ,, =Formula
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/gmail/skype: - http://tanbircox.blogspot.comSolution:X = 1 1 ,, ,,
= Y = 1 1 ,, ,, = = = =,, ,, 100 ,, ,, ,, = ( ) 00Formula =( )=( )
00Solution: = (380+20) 400 400 =20 ,, 100 ,, ,, ,,Solution:10% =
(100-10) 90 5% = (100+5) 105 = (105 90) 15 15 100 ,, 45 ,, ,, ,, ,,
300
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/gmail/skype: - http://tanbircox.blogspot.comSolution:20% =
(100+20) 120 10% = (100-10) 90 20% , 100 = 120 ,, 90 ,, ,, ,, =(
)=108 % , = (100 ) = (100 ) 312 =100 ,, 31 ,, ,, ,, ,, =
200Solution:x % , = 00 ( 00 ) = 100 ,, n ,, ,, ,, =y % , = 00 100 =
( 00 ) ,, ,, ,, ,,=( )( ) = n ( )( )
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/gmail/skype: - http://tanbircox.blogspot.comSolution:36 =12 100 ,,
,, ,, 20% , 100 = (100 + 20) 120 20% , = 120 20 ,, ,,
,,Solution:15% 1200 + 1200 15% (1200 15100) 1200+180 = 13805% 1380
1380 5% 1380 69 = 1311 Solution:5 = 2 100 ,, ,, = 4040% ,100
(100+40) 140 140 =40 35 ,, ,, ,, ,, = 10
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/gmail/skype: - http://tanbircox.blogspot.comSolution:12 =20 1 ,,
,, ,, = 53 1 = = 2 53=1353 =13 ,, 100 ,, ,, 20 [ ]Solution:3 = 1 1
,, ,, ,, = 2 = 1 1 ,, ,, ,, =2 1 = =1213=16[ ]13 =16 ,, 100 ,, ,,
50
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/gmail/skype: - http://tanbircox.blogspot.comSolution:, 5 = x 1 ,,
,, ,, = 4 = x 1 ,, ,, ,, = 1 = = = = ,, 100 ,, ,, 25
- 52. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.com1 Lac = 1051 Million =
106= 10 lac1 Crore =107=10 million1 Billion = 109(USA) =1012(Eu)1
Trillion = 1012(USA) = 1018(Eu)1 kilogram= 2.2 (lbs) pounds1 Seer =
.93 kg1 mound = 40 seer = 37.2 kg1 quintal = 100 kg1 ton = 1000
kgS.I International Systems of Units 1960 CGS Centimeter . Gram
.SecondM.K.S Meter . Kilogram . SecondF.P.S Foot .Pound .Second12
Inch = 1 foot , 3 foot = 1 Yard , 1760 Yard = 1
mileRelationshipDistance Area Volume1 Inch = 2.54 Centimeter 1
Inchs2= 6.45 cm21 liter = 1000 Cubic Centimeter1 Meter = 39.37 Inch
1 Hectare = 10000 meter21 Cubic meter = 1000 liters1 mile = 1.61
kilometer 1 Katha = 720 feet21 Cubic foot = 28.31 liters1 Nautical
Mile = 1.853km 1 Acre = 4047 meter21 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 Y[r^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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- 54. Want more Updates http://facebook.com/tanbir.ebooksfacebook
/gmail/skype: - http://tanbircox.blogspot.com 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 :, A= q n, q = n =(, , W = q x n, q = ,n = x =w = n x, d = v
t., v = t=, Q(t) = Q0 q t, Q0= q = t= Q(t) = t ( + )P = b r, b =r =
= = S%P= = b S%
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