Average Concept For Competitive Exams

Average Concepts And Problems In Aptitude For Competitive Exams Like CAT, IIT, IBPS Bank PO, Campus, GMAT, Gate And Other Competitive Exams.
1.Average = Sum Of Objects/Number Of Objects
We Can Say Average As a Airthmetic Mean.
2.Lets We Can Take, A Person Travel Certain Length At P Kmph and Same Distance Q Kmph Then
Average = 2PQ/P+Q
3.If we Take n1 Quantities Is P and n2 Quantities Is Q Then,
Average = (n1*P+n2*Q)/n1+n2
4.If All Values Are Same, Then Average Is That Same Number.
5.If We Have Many Of Number And We Increase Some Value To each Number Then There Is Same Increase In Average.
6.If We Have Many Of Number And We Multiply Some Value To each Number Then There Is Same Multiplication In Average.
7.If There Is An Airthmetic Series And Numbers Are Odd, Then Mid Value Is Average.
Example: 2 4 6 8 10
Then Its Average Is 6




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Probablity Concepts And Problems In Aptitude For Competitive Exams

Probablity Concepts And Problems In Aptitude For Competitive Exams Like CAT, IIT, IBPS Bank PO, Campus, GMAT, Gate And Other Competitive Exams.

Probablity Is Basically A Possibility Of Event To Occur.We Can Say This Chance.We Will Represent Probablity As P.

There Are Some Terminologies, That Would Be Used In Probablity Concept.
1.Random Experiment: It Is Also Called Trial Event.Suppose We Draw Five Cards From Well Shuffled 52 Cards, Then Occurance Of Ace And King Are Random Experiment.
2.Mutually Exclusive Event: Two Events, That Are Not Happened At Same Time Are Called Mutually Exclusive Events.Suppose We Toss A Coin, Then Occurance Of Head Or Tail Are Not At Same Time.These Occurance Are Called Mutually Exclusive Events.
3.Equally Likely Events: When We Toss The Coin, There Is Same Probablity Of Occurance Of Head And Tail. Then Occurance Of These Events Are Called Equally Likely Events.
4.Independent Events: Two Events Are Called Independent Events, When Occurance Of Any One Event Not Affect On Occurance Of Others.Suppose We Have Basket Of Fruits And We Withdraw One And Replace By Other And In Again In Second Chance We Withdraw Another Fruit, Then These Both Events Are Called Independent Events.
Probablity Important Formulas And Terms:
P(E) = Number Of Favorable Events/Total Number Of Events
P(E) = n(E)/n(S) = m/n
P(E) = 1 – P(Bar E)
P(Bar E) = 1-m/n = n-m/n
Addition Theorem In Probablity
When There Are Two Events E1 And E2 Then P(E1UE2) = P(E1)+P(E2)-P(E1)IntersectionP(E2)
If These Two Events Are Mutually Exclusive, Then
P(E1UE2) = P(E1)+P(E2)



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Permutations And Combinations Concept For Competitive Exams

Permutations And Combinations Concept For Competitive Exams Like CAT, GMAT, IBPS Bank PO, IT Officer, SSC And Other Government Exams.

Permutation Is Basically Known As Arrangements.Suppose We Take Four Elements And Choose Two In These Elements Then Arrangement Made Is 12.
Permutation Is Divided Basically In Two parts:
1.Linear Permutation
2.Circular Permutation

Permutation is Also Termed As Linear Permutation. And Denoted As P
npr = Number Of Permutations With n Different Things Taken r at a time.
npr = n(n-1)(n-2)(n-3)(n-4)……….(n-r+1) = n!/(n-r)!
n! = Factorial Of n
0! = 1
1! = 1
2! = 2*1 = 2
3! = 3*2*1 = 6
If There Are N Different Things And M Groups Of Different Things,And Basically Objects Are Like a1, a2, a3…………..am Then
N!/(a1!)(a2!)……….(am!)
When We Take Elephant Then Permutation = 8!/2!
Notes: In Permutation Order Is Very Important.
2.Circular Permutation: In Circular Permutation Objects Are Arranged In Circular Way. And Circular Permutations Of N Things, All Are Taken At A Time: (N-1)!.
………………………………………………………………………………………………………………………………………………………………………………………
Combination: Combination Is Basically Termed As Selections.And Order Is Not Important In Selection.We Can Write ncr as n Different Things Taken r at a Time.
ncr = n!/(n-r)!r!
ncr = nc(n-r)
nco = 1
nc1 = n
ncn = 1
In Above Description In ncr, n is superscript
c is combination
r is subscript.
In Above Description In ncn, n is superscript
c is combination
n is subscript.


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Profit And Loss Concept In Aptitude For Competitive Exams

Profit And Loss Concept And Problems For Competitive Exams Like CAT, SSC, IBPS Bank PO, IAS, Gate, Company Campus Exams And Other Government Exams.

First Of All We Take Basic Terminologies For The Profit And Loss Topic:
1.Selling Price(SP): The Price On Which Object Would Be Sold, Is Called Selling Price.We Will Represent Selling Price As SP.
2.Cost Price(CP): The Price On Which, Object Is Purchased, Would Be Called Cost Price.We Will Represent Cost Price As CP.
3.Profit(P): When Any Person Sold A Particular object Greater Amout Than He Purchased Then He Got Profit(P).Profit Is Denoted As P.
4.Loss(L): when Any Person Sold Object Smaller Price Than He Purchased Then That Person Got Loss Definitely.
5.Marked Price(MP): The Price Mentioned On The Object Is Called Marked Price. List Price Is Treated As Its Synonym.
6.Discount: It Is The Reduction On Marked Price Provided By The Seller To The Customer.It Is Write As d.
…………………………………………………………………………………………………………………………………………………………………………………….
Important Formulas On Profit And Loss:

• Profit(P) = Selling Price – Cost Price = SP – CP
• Profit Percentage = [(Profit)/Cost Price]*100
• Selling Price(SP) In Profit = [(100+Profit Percent)/100]*Cost Price(CP)
• Loss(L) = Cost Price(CP) – Selling Price(SP) = CP -SP
• Loss Percentage = [(Loss)/(Cost Price)]*100
• Selling Price(SP) In Loss = [(100-Loss Percent)/100]*Cost Price(CP)
• Discount(d) Percentage = d% = (Discount/ Marker Price)*100
• Selling Price(SP) = [(100-d%)]/100*MP

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Mensuration In Aptitude For Competitive Exams

Mensuration In Aptitude For Competitive Exams Like CAT, SSC, IBPS Bank PO, IAS, Gate And Other Government Exams.

In This Mensuration Topic, We Will Focus On The Geometry Concepts.
1.Triangle: The Geometry Consist Three Sides Called Triangle.
Types Of Triangle: There Are basically Three Types Of Triangle, When We Consider Their Sides.
A.Equilateral Triangle: The triangle Of Which Three Sides Are Equal, Called Equilateral Triangle.In Equilateral Triangle All Sides Are Equal And All Angles Are Equal.Angle Is Of 60 Degree.
B.Isosceles triangle: In Isosceles Triangle Two Sides And Opposites Angles Are equal.
C.Scalene Triangle: In This Triangle All Sides And All Angles Are Unequal.
There Are Basically Three Types Of Triangle, When We Consider Angles:
A.Acute Angled triangle: All Of Three angles Are Less Than 90 Degree.
B.Obtuse Angled triangle: A triangle In Which One angle Is Greater Than 90 Degree.
C.Right Angled triangle: In Right Angled Triangle One Angle Is Of 90 Degree.

Formulas And Concepts For Triangle:
1.Sum Of All Angles Of A triangle Is Of 180 Degree.
Let Us Take Angle Of triangle Is A, B And C Then
A+B+C = 180Degree
2.Area Of Triangle = 1/2*Base*Height.
3.Area Of Equilateral Triangle: [(3^1/2)/4* (Side)*2] = We Can Read This Root 3 By 4 Multiplied By Side Square.
4.Sum Of Two Sides Of A Particular Triangle Is Always Greater Than Third Side.
5.Hero Formula For Triangle: [s(s-a)(s-b)(s-c)]^1/2
Where s = (a+b+c)/2
a, b, c Are The Sides Of Triangle.
2.Rectangle Concepts And Formulas:
Rectangle Is An Area Or Geometry Of Which Opposite Sides Are Equal And All Angles Are Of 90 Degree.

• Rectangle Area: Length*Breadth.
• Rectangle Perimeter: 2*[Length+Breadth].
• Rectangle Diagonal: [(Length)^2 + (Breadth)^2]^1/2
• Area Of Room Of Four Walls: 2*Height*[length+height]

3.Concepts And Formulas On Square:
A Square Has All Sides Equal And All Angles Are Of 90 Degree.

• Area Of Square: (Side)^2 = 1/2*(Diagonal)^2.
• Perimeter Of Square: 4*Side.
• Length Of Diagonal: Side*1.414

4.Concepts And Formulas Of Quadilateral:
Sum Of Angles Of Quadilateral Is 360 Degree.

• Quadilateral Area Is Base* Height.
• Quadilateral Perimeter: 2[Base+Height].

5.Concepts And Formulas On Parallelogram:
A Parallelogram Is A Geometry In Which Opposite Sides Are equal.

• Area Of paralleogram: Base * Height.
• Perimeter Of paralleogram: 2*(Base+Height).

6.Concepts And Formulas On Rhombus:
A Rhombus Is Structure Or Area In Which, All Sides Are Equal.

• Area Of Rhombus: 4 * Side.
• Area Of Rhombus: 1/2*(Product Of Diagonals) = 1/2*d1*d2.
• Diagonal 1 = d1
• Diagonal 2 = d2

7.Concepts And Formulas On Circle And Semicircle:
When We take Radius = r
Then Area Of Circle = Pi*r^2 (Pi = 3.14)
Circle Circumference = 2*Pi*r
Circle Diameter = 2*r
Semi-Circle Area = (Pi*r^2)/2
Semi-Circle Circumference = (pi*r+2*r)
8.Concepts and Formulas On Trapezium:
Trapezium Area = 1/2*(Sum Of Parallel Sides)* Distance Between parallel Sides.



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Circular Track Problems In Aptitue For Competitive Exams

Boats And Stream Problems In Aptitude For Competitive Exams Like CAT, SSC, IBPS Bank PO, IAS, Gate And Other Government Exams.

Concept Of Circular track Problems:
Condition 1: When Two Person With Speed S1 Km/hour And S2 Km/hour, Starting With A Same Position On The Circumference Of Track C Km In Same Direction, Then
A.Time Taken For Meeting First Time At Any Position: (C/S1-S2) Hour
B.Time Taken For Meeting At Starting Point, At First Time:
LCM(C/S1.C/S2)hour.
Condition 2: When Two Person With Speed S1 Km/hour And S2 Km/hour, Starting With A Same Position On The Circumference Of Track C Km In Opposite Direction:
A.Time Taken For Meeting First Time At Any Position: (C/S1+S2) Hour
B.Time Taken For Meeting At Starting Point, At First Time:
LCM(C/S1.C/S2)hour.
Notes1.We Can Use The Concept Of Time  Speed And Distance For Convering Km/hour To Metre/ Second Or Vice Versa
Notes2: When We Consider Sign Of Above Formula Then This Is Same As Rail Problem.
Notes3: In Rail And Circular Track Problem In Same Direction We Use – Sign And For Opposite Direction We Use + Sign. But In Stream And Boats Problem Converse Is True.




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Boats And Streams Problems In Aptitude For Competitive Exams

Boats And Stream Problems In Aptitude For Competitive Exams Like CAT, SSC, IBPS Bank PO, IAS, Gate And Other Government Exams.

Concepts On Boats And Streams Problem:
1.When Boat And Water Stream Move In One Direction Then This Is Called Boat Is Moving Downstream.The Total Speed Of Boat Would Increased In This Condition.
2.When Boat And water Stream Are Moving In Opposite Direction Then Boat Is Called Moving Upstream.The Total Speed Of Boat Would Decreased In This Condition.
Let, Speed Of Boat In Constant Water = S1
Speed Of Water Stream = S2

Formula1: Speed Of Boat In DownStream Condition = (S1+S2)Km/hour

Formula2: Speed Of Boat In Upstream Condition = (S1-S2)Km/hour

Notes: This Is The Advice Of Author To Learn The Formula. When We Concentrate On the Sign Of Above Formulas, These Are Different From Rail Problems.In First Formula water Stream And Boat Is in Same Direction But Sign Is + Not Minus Like Rail Problems.
This Is The Key For Learning These Formulas And Remove Confusion About These Problems.
Important Formulas:
If We Take Speed In Downstream Condition = S1 Km/hour
Speed In upstream Condition = S2 Km/hour

• Speed In Constant Water = 1/2(S1+S2) Km/hour.
• Rate Of Stream: 1/2(S1-S2) km/hour.

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Time Speed And Distance Concepts In Aptitude For Competitive Exams

Time And Distance Concepts In Aptitude For Competitive Exams Like CAT, SSC, IBPS Bank PO, IAS, Gate  And Other Government Exams.

1.Relation Between Time, Distance And Speed:
Speed = Distance/Time

• Speed Is Measured In Metre/Sec Or Kilometre/Hour.
• Time Is Measured In Second Or Minute Or Hour.
• Distance Is Measured In Metre Or Kilometre.

2.Some Speedy Math Methods To Convert Km/hour To Metre/Sec And Vice Verse:
A.To Convert Km/Hour To Metre/Sec: Km/Hour*5/18 = M/Sec.
B.To Convert Metre/Sec To Km/Hour: Metre/Sec*18/5 = Km/Hour.
3.Concept Of Average Speed:
Average Speed = (Total Distance Traversed/ Total Time In Traversing Distance).
4.Some Important Conditions For Solving Problem Immediately.
A. If Some Distance Is Covered By One Person By Speed P km/hour, And Another Same Distance Is Covered By Q km/hour.
Then
Average Speed = 2PQ/(P+Q) = Harmonic Mean Of Both
B.If Three Equal Distance Is Covered By Speed P Km/hour, Q Km/hour And R km/hour,
Then Average Speed = 2PQR/(PQ+QR+RP)Km/hour = Harmonic Mean Of Above Three.
C. If Three Same Distance Is Covered By P Km/hour, Q km/hour And R km/hour And Takes Equal Amount Of Time Then The
Average Speed = (P+Q+R)/3 Km/Hour.
D. If Two Same Distance Is Covered By P Km/Hour, Q Km/hour In same Amount Of Time, Then
Average Speed = (P+Q)/2 Km/hour.
5.Ratio Relation Among Time, Distance And Speed:
If Speed Of  Ram And Ramesh In The Ratio Of P/Q Then Distance Traversed By These Person In The Ratio P/Q And Time Contained In The Ratio Of Q/P.
6.Relative Speed Comcept:
If Two Objects Are Moving In Same Direction With P Km/hour And Q Km/hour Then
Relative speed = (P-Q)Km/hour If P>Q
(Q-P)Km/hour If Q>P
If Two Objects Are Moving In Opposite Direction With Speed P Km/hour And Q km/hour Then
Relative Speed = (P+Q)Km/hour.

Notes: Two Bikes B1 And B2 Starts From Home H1 And H2 And Reached To H2 And H1 By Travelling Towards Each Other And Take Time T1 And T2 Then Their Raito Of Speed = T2^1/2/T1^1/2 = (Underroot Of T2/Underroot Of T1)
7.Train Relative Speed Problems:
A. Moving Train And Stationary Object Problem
There Are Two Conditions For Moving Train And Stationary Object Prblems.
Condition 1: When Object Traversing By Train Is Negligible.
When Train Is Tavelling Towards Pole Or Other Neglegible Length Object And Cross The Particular Object Then
Speed Of The Train = (Length Of The Train)/Time taken To Traversing The Pole)
When We Take Speed = S, Length Of The Train = L, Time Taken To Cross The Pole = T
Then Formula Of Speed Would Become S = (L/T).
Condition 2: When Object Traversing By Train Is Not Negligible.
When Train Is Travelling Towards The Length Object,And
Length Of The Train = L
Length Of The Object = K
Time For Crossing The Object= T
Then, The Speed Of Train For Crossing The Object Is:
Speed = [(Length Of Train + Length Of Object)/Time Take For Crossing The Length Object]
S = (L+K)/T.
B.Moving Train And Moving Object Of Negligible Length:
Condition 1: When Train And Moving Object(Zero Length) Are Moving Towards Each Other With Respective Speeds P And Q Then
Relative speed = (P+Q).
(P+Q) = [Length of The Train/Time Taken For Crossing The Object].
When We Take Length Of Train = L
Time Taken For Crossing The Object: T
(P+Q) = L/T
Condition 2: When Train And Moving Object(Zero Length) Are Moving In Same Direction With Speed P And Q Then
Relative Speed = (P-Q) = [Length Of Train/Time Taken For Crossing Each Other]
Take Length Of Train = L
Time Taken For Crossing The Object: T
Relative Speed = (P-Q) = L/T.
C:Moving Train And Moving Object Of Some Length
Condition1:When Train Of Length L1 And Moving Object Of Length L2 Are Moving Each Other With Speed P And Q Then,
(P+Q) = [(Length Of Train + Length Of Moving Object)/ Time Taken For Crossing Each Other]
(P+Q) = [L1+L2]/T
Condition 2:When Train Of Length L1 And Moving Object Of Length L2 Are Moving In Same Direction With Speed P And Q Then
(p-Q)= [L1-L2]/T




Quantities aptitude questions given here are extremely useful for all kind of competitive exams like Common Aptitude Test (CAT),MAT, GMAT, IBPS 

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Competitive Exams, L.I.C/ G. I.C Competitive Exams , Railway Competitive Exam, TNPSC, University Grants Commission (UGC), Career Aptitude Test 

(IT Companies) and etc, Government Exams etc ,Quantitative Aptitude For Competitive Examinations by R. S. Aggarwal , Quantitative Aptitude Book 

Description. Quantitative Aptitude for Competitive Examination (Fully Solved) Bank P.O, S.B.I. P.O; I.B.P.S; R.B.i. Exam

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Important General Knowledge Questions 2013 for IBPS PO III

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