Aptitude Questions

1. “WORK IS WORSHIP”
Welcome To
JSpiders
Aptitude
Quantitative General Reasoning
Aptitude English

2. PREFACE
We are all set to start Quantitative Aptitude and so, first we must know:
 What is Aptitude
 What is Aptitude Test and
 why IT companies have kept aptitude test as the first road block to be cleared to
proceed to the
next round.
Aptitude is a natural ability to do something or to learn something or in other words it is inclination or
capacity for learning. And Aptitude test is a standardized test designed to predict an individual’s ability
of learning skills. How fast an individual can learn skills and how efficiently he can deliver it. And this is
what makes it very important. Once you cleared the Aptitude test you will get required momentum to
sail through next stages as well. It will provide enough confidence and right attitude and glory will be
yours.
Well biggest roadblock in doing aptitude is lack of interest shown by students. And most of the time I
have seen that instead of having all technical skills, students fail to deliver at aptitude. Let me tell you
if you understand how to approach it will be one of your very strong points.
To make it easier I have made two parts to be focused on.
Preparation Part Personal Part
1. Calculation 1. Self- motivation and determination
2. Relation or Relate the given quantity 2. Perseverance.
3. Trick 3. Right guidance and
4. Speed 4. Horripilation.
5. Hitting the right question and
6. More and more tricks

3. Once I come to this point and explain it all, you will discover yourself how it works.
I will always endeavor to deliver my best and once I am completed, I will strive not to leave any
place for skepticism. My effort will be to make it as interesting as possible.
Our student's constructive feed back and suggestions are most welcome and highly appreciated.
I will be highly obliged if you message /email me your feedback or suggestion on
shambnu060@gmail.com.
S Kumar
CONTENTS
1. Basics
2. Number System
3. H C F and L C M
4. Simplification
5. Square Roots and Cube Roots
6. Average
7. Problems on Numbers
8. Problems on Ages
9. Percentage
10. Profits and Loss
11. Ratio and Proportion
12. Partnership
13. Chain Rule
14. Time and Work
15. Pipes and Cistern
16. Time and Distance
17. Problems on Train
18. Boats and Streams
19. Allegation or Mixture
20. Simple Interest and compound Interest
21. Area, Surface Areas and Volumes
22. Clocks
23. Permutations and Combinations
24. Probability
25. Heights and Distances (Trigonometry)
26. Odd man out Series
27. Geometry
28. Data Interpretation
29. Races
30. Calendar
31. Series
32. Set Theory
33. Linear Equations
34. Quadratic Equation

4. IMPORTANT POINTS AND FORMULAS
1. Number System
I. Divisibility Rules
II. Unit digit numbers
2. H.C.F and L.C .M
I. Product of two numbers = HCF×LCM
3. Average
I. Average =
𝐒𝐮𝐦 𝐨𝐟 𝐎𝐛𝐬𝐞𝐫𝐯 𝐚𝐭𝐢𝐨𝐧
𝐓𝐨𝐭𝐚 𝐥 𝐧𝐨 𝐨𝐟 𝐨𝐛𝐬𝐞𝐫𝐯𝐚 𝐭𝐢𝐨𝐧𝐬
II. If a man covers a certain distance at x kmph and an equal distance at y kmph
Then the average speed during the whole journey =
𝟐𝒙𝒚
𝒙+𝒚
𝒌𝒎𝒑𝒉
4. Percentage
I. x % =
𝑥
100
II. If the price of commodity increases by R% then the reduction in consumption so as not to increase the
expenditure is= [
𝑹
𝟏𝟎𝟎 +𝑹
× 𝟏𝟎𝟎] %
III. If the price of a commodity decreases by R% then the increase in consumption so as not to decrease the
expenditure is= [
𝑹
𝟏𝟎𝟎 −𝑹
× 𝟏𝟎𝟎] %
IV. Let the population of a town be now be P and suppose it increases at the rate of R% per year then
 Population after n years = 𝑷 ( 𝟏 +
𝑹
𝟏𝟎𝟎
)
𝒏
 Population n years ago =
𝑷
𝑷( 𝟏+
𝑹
𝟏𝟎𝟎
)
𝒏
V. Results on depreciation : Let the present value of a machine be P suppose it depreciates at the rate of
R% per anum then:
 Value of the machine after n years= = 𝑷 ( 𝟏 −
𝑹
𝟏𝟎𝟎
)
𝒏
 Value of the machine n years ago=
𝑷
𝑷( 𝟏−
𝑹
𝟏𝟎𝟎
)
𝒏
VI. If A is R% more than B, then B is less than A by [
𝑹
𝟏𝟎𝟎+𝑹
× 𝟏𝟎𝟎] %

5. VII. If A is R% less than B, then B is more than A by [
𝑹
𝟏𝟎𝟎−𝑹
× 𝟏𝟎𝟎] %
5. Profit and Loss
C.P = cost price S.P = Selling Price
I. 𝑮𝒂𝒊𝒏 = 𝑺. 𝑷 − 𝑪. 𝑷 and Gain% = (
𝑮𝒂𝒊𝒏
𝒄.𝒑
× 𝟏𝟎𝟎)
II. 𝑳𝒐𝒔𝒔 = 𝑪. 𝑷 − 𝑺. 𝑷 and Loss% = (
𝑳𝒐𝒔𝒔
𝒄.𝒑
× 𝟏𝟎𝟎)
III. S.P when
 There is profit 𝑺. 𝑷 =
(𝟏𝟎𝟎+𝑮𝒂𝒊𝒏%)
𝟏𝟎𝟎
× 𝑪. 𝑷
 There is loss 𝑺. 𝑷 =
(𝟏𝟎𝟎 −𝒍𝒐𝒔𝒔%)
𝟏𝟎𝟎
× 𝑪. 𝑷
Sequestered:- (of a place or person) isolated and hidden away, secluded, cloistered, cut off, secret
To seize property until a debt has been paid
IV. C.P when
 There is profit 𝑪. 𝑷 =
𝟏𝟎𝟎
(𝟏𝟎𝟎 +𝑮𝒂𝒊𝒏%)
× 𝑺. 𝑷
 There is loss 𝑪. 𝑷 =
𝟏𝟎𝟎
(𝟏𝟎𝟎 −𝒍𝒐𝒔𝒔%)
× 𝑺. 𝑷
6. Ratio and Proportion
I. Ratio: - The Ratio of two quantities a and bin the same units is the fraction
𝑎
𝑏
and written as a: b.
II. Proportion:- The equality of two ratios is called proportion so a:b = c:d
III. Fourth proportional: - If a: b=b: c,then c is called the fourthproportional of a, b and c.
IV. Third proportional: - If a: b= b: c, then c is called the third proportional.
V. Mean proportional:- Mean proportional between a and b is √ 𝒂𝒃
VI. Duplicate ratio of (a:b)is (𝒂 𝟐, 𝒃 𝟐)
VII. Sub – Duplicate ratio of (a:b)is (√ 𝒂,√ 𝒃)
7. Partnership
I. Ratio of division of Gains:
i. When investment of all partners are forthe same time. The gain or loss is distributed
among the partners in the ratio of their investments.
ii. When investments are made fordifferent time periods , then the equivalent capitals time
periods then the equivalent capitals are calculatedfor a the given investments. Suppose a
invests X for P months and B invests Y forQ months , then
(A'S share of profit) :(B’S share of profit) = XP:YQ
8. Time and Work
I. If A can do a piece of work in n days then A'S 1 day’s work = 1/n
II. If A'S 1 days work = 1/n then A can finish the work in n days
III. If ratio of work done by A and B is 3:1
Then ratio of time taken by A and B to finish the work is 1: 3
9. Pipes and Cisterns
I. Inlet: - A pipe connected with a tank, a cistern or a reservoir that fills it is known as an inlet.
II. Outlet:- A pipe connected with a tank, a cistern or a reservoir emptying it is known as an outlet.

6. III. If a pipe can fill a tank in x hours then part filled in 1 hour = 1/x
IV. If a pipe can empty a full tank in y hours then
Part emptied in 1 hour = 1/y
V. If a pipe can fill a tank in x hours and and other pipe can empty the full tank in y hours (y>x) , then opening
both the pipes the net part filled in 1 hour
=
𝟏
𝒙
−
𝟏
𝒚
VI. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (x>y) .Then opening
both the pipes the net part emptied in 1 hour
=
𝟏
𝒚
−
𝟏
𝒙
Proponent:- a person who advocates a theory or proposal, advocate, protagonist, supporter, patron, apostle
10. Time andDistance
I. Speed =
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑇𝑖𝑚𝑒
, time =
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑆𝑝𝑒𝑒𝑑
, Distance = (speed × time)
II. x km/hr = ( x×
𝟓
𝟏𝟖
)m/sec and x m/s = (x×
𝟏𝟖
𝟓
)km/hr
III. If the ratio of the speeds of A and B is a:b,then the ratio of the time taken by them to coverthe
same distance is
1
𝑎
:
1
𝑏
or b:a
IV. Suppose a man covers a certain distance at x km/hrand an equal distance at y km/hr, then the
average speed during the whole journey is (
𝟐𝐱𝐲
𝐱+𝐲
)km/hr.
11. Problemsintrains
I. If a train of length L meters is to pass a man, a pole or a signal post then distance travelled by train is L
meters.
II. If a train of length L meters is to pass a stationary object of B meters then distance covered by train is
(L+B) meters.
III. If two trains of speed u m/s and v m/s are moving in the same direction then their relative speed
= (u-v) m/s where (u>v)
IV. If two trains of speed u m/s and v m/s are moving in the opposite direction then their relative speed
= (u + v) m/s
V. If two trains of length a meters and b meters are moving in opposite directions at u m/s and v m/s, then
time taken by the trains to cross each other = (
𝐚+𝐛
𝐮+𝐯
)sec
VI. If two trains of length a meters and b meters are moving in the same direction at u m/s and v m/s (u>v)
then time taken by faster train to cross the slower train = (
𝐚+𝐛
𝐮−𝐯
)sec

7. VII. If two trains start at the same time from points A and B towards each other and after crossing they take a
and b sec in reaching B and A respectively then ( A'S speed) :(B'S speed) = (√𝒃: √𝒂)
12. Boatsand Streams
I. Downstream:- the direction of boat along the stream is called downstream.
II. Upstream:- The direction of boat against the stream is called upstream.
If the speed of a boat in still water is u km/hr and speed of the stream is v km/hr then
 Speed downstream = (u + v)km/hr
 Speed upstream = (u-v) km/hr
III. If the speed downstream is a km/hr and speed upstream is b km/hr then
 Speed of boat in still water =
𝟏
𝟐
(a + b)km/hr
 Speed of stream =
𝟏
𝟐
(a-b)km/hr
Desultory:-lackingpurposeorenthusiasm,lukewarm,haphazard,erratic ,unmethodical
13. AlligationorMixture
C.p of a unit of cheaper item c.p of a unit of dearer item
Mean price
d - m m - c
so, (cheaper quantity):(dearer quantity )= (d-m ) : (m-c)
 Suppose a container contains x units of liquid from which y units are taken out and replaced by water. After
n operations, the quantity of pure liquid
=[𝒙 ( 𝟏 −
𝒚
𝒙
)
𝒏
] units
14.SIMPLE INTERESTAND COMPOUND INTEREST
I. S.I=
𝑷×𝑹×𝑻
𝟏𝟎𝟎
II. Compound interest
Let Principal=P, Rate=R% and Time=n years
i. Amount=P= 𝑷 ( 𝟏 +
𝑹
𝟏𝟎𝟎
)
𝒏
[when interest is annually]
And C.I= A-P
ii. A=P= 𝑷 ( 𝟏 +
𝑹
𝟐×𝟏𝟎𝟎
)
𝟐𝒏
[when interest is half-yearly]
And C.I=A-P
III. When rates are different for different years, say R1%, R2% and R3% for 1st, 2nd and 3rd year respectively
Then amount= P( 𝟏 +
𝑹𝟏
𝟏𝟎𝟎
) ( 𝟏 +
𝑹𝟐
𝟏𝟎𝟎
) ( 𝟏 +
𝑹𝟑
𝟏𝟎𝟎
)

8. 15.Area, SurfaceArea and Volume
I. Rectangle
 Areaof Rectangle= Length× Breadth
So length=Area/Breadth and Breadth=Area/Length
 Perimeter of Rectangle=2(L+B)
II. Square
 Areaof square=( 𝒔𝒊𝒅𝒆) 𝟐 =
𝟏
𝟐
( 𝒅𝒊𝒂𝒈𝒐𝒏𝒂𝒍) 𝟐
 lengthof diagonal ofasquare=√2×side
III. Triangle
 Areaof a triangle=
𝟏
𝟐
×Base× Height
 Areaof a Triangle=√ 𝐬(𝐬 − 𝐚) (𝐬 − 𝐛) (𝐬 − 𝐜)
Truncate:- shortenby cutting offthe top orthe end , curtail, retrench
Where a, b, c are the side of the triangle and s=
𝑎+𝑏+𝑐
2
 Areaof an equilateral triangle=
√ 𝟑
𝟒
×𝒔𝒊𝒅𝒆 𝟐
 Radius of an in circleof an equilateral triangle of side a=
𝑎
2√3
 Radius of circumcircle of an equilateral triangle of side a=
𝑎
√3
IV. Quadrilateral
 Areaof a parallelogram=Base× height
 Areaof a rhombus=
𝟏
𝟐
(productofdiagonals)
 Areaof a Trapezium=
𝟏
𝟐
(sumofparallel sides× distancebetweenthem)
V. Circle
 areaof a circle= 𝝅𝒓 𝟐
 Perimeterof a circle=2 𝝅r
 lengthof anarc of circle=
𝜽
𝟑𝟔𝟎
×2 𝝅r (where 𝜽 isthe central angle)
 Areaof a sector==
𝜽
𝟑𝟔𝟎
× 𝝅𝒓 𝟐
 Areaof a semi-circle=
𝝅𝒓 𝟐
𝟐
 Circumferenceofasemi circle= 𝝅r
 Perimeterof a Semi-circle= 𝝅r+ 2r
VI. CUBOID
 Volume of a cuboids =(l×b×h) cubic units
 Surface area=2(lb+bh+hl) Sq.units
 Diagonal=√𝑙2 + 𝑏2 + ℎ2 units
 Area of 4 walls of a cuboid=2(l+b)×h sq.units

9. VII. CUBE
 Volume= 𝑎3 cubic units
 Surface Area= 6𝑎2 sq. Units
 Diagona=√3 a units
VIII. CYLINDER
 volume=( 𝝅𝒓 𝟐 𝐡)cubicunits
 Curvedsurfacearea= 2 𝝅rhsq. Units
 TSA=2 𝝅𝒓 𝟐+2 𝝅𝒓𝒉= 2 𝝅r(h+r)sq.units
IX. CONE
 SlantheightL=√ 𝒉 𝟐 + 𝒓 𝟐
 Volume=
𝟏
𝟑
𝝅𝒓 𝟐 𝐡cubicunits
Inoculate:-immunize,vaccinate, safeguardagainst
 CurvedSurfaceArea= 𝝅rl sq. Units
 TSA=( 𝝅rl+ 𝝅𝒓 𝟐)sq.Units
X. SPHERE
 Volume=
𝟒
𝟑
𝝅𝒓 𝟑cubicunits
 SurfaceArea=(4 𝝅𝒓 𝟐)sq.units
XI. HEMISPHERE
 Volume=
𝟐
𝟑
𝝅𝒓 𝟑cubicunits
 CSA=2 𝝅𝒓 𝟐 squnits
 TSA= 𝟐𝝅𝒓 𝟐 + 𝝅𝒓 𝟐=3 𝝅𝒓 𝟐 sq units
Note: 1𝒎 𝟑= 1000litre
1000𝒄𝒎 𝟑=1 litre
16. CLOCKS
 Angletracedby minute handin 60min=360°
So anglemadein min=
𝟑𝟔𝟎
𝟔𝟎
=6°
Everyminute minutehand makes6° angle
 Angletracedby hourhandin 60 min=30°
so angletracedby hourhandin 1 min =
𝟑𝟎
𝟔𝟎
=(
𝟏
𝟐
)
°

10. Everyminutehourhand ofa clockmakes (
𝟏
𝟐
)
°
 In 60 minutes, the minutehand gains55minutes onthe hourhand.
17. PERMUTATIONS AND COMBITIONS
 n!=n(n-1)(n-2)......3.2.1
e.g.: 6!= 6*5*4*3*2*1
 Permutation: The different arrangements of a given number of things by taking some or all at a
time, are called permutation.
 No. of permutations= No of permutations of n things taken r at a time is
nPr=
𝒏!
( 𝒏−𝒓)!
e.g.: 6P2=6!/4!=6*5*4!/4!=30
Peruse:- read orexaminethoroughlyorcarefully,scrutinize,wadethorough
 Combination: Eachof the different groups or selection which can be formed by taking some or all
of a number of objects is called a combination.
No. of combination: the no of all combination of n things, taken r at a time is
nCr=
𝒏!
𝒓!( 𝒏−𝒓)!
Note: nCn=1 and nC0=1
e.g.: 11C4=11!/4!*7!=330
18. PROBABILITY
 Probability is the measure of the like hood that an event willoccur.
Probability is quantified as a number between 0 and 1. The higher the probability of an event, the
more certain we are that the event will occur.
 ProbabilityP(E)=
𝑭𝒂𝒗𝒐𝒖𝒓𝒂𝒃𝒍𝒆 𝒐𝒖𝒕𝒄𝒐𝒎𝒆
𝑻𝒐𝒕𝒂𝒍 𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆 𝒐𝒖𝒕𝒄𝒐𝒎𝒆
Coin
 If a coin is tossed then total outcome=[H,T]
 If twocoins are tossed then total outcomes = HH,HT,TH,TT
 Forthree coinstotal Outcomes=HHH,HHT,HTH, HTT,THH, TTH,THH,TTT
 If two diceis thrownthen total possible outcomes=6×6=36
 A packof cardshas52 cards.
 Thereare13 cardsof each suit namely.
 Spades,clubs,hearts anddiamonds.
 Spadesandclubsare blackcards.
 Heartsand diamondsareredcards.
 Aces, kings,queensandjacksare calledfacecards.
 So total no. Of facecards=4×4=16.

11.  Eachcard is 4 in number.
19. TRIGNOMETRY
 ℎ2 = 𝑝2 + 𝑏2
 sin𝜃=
𝑝
ℎ
cosec𝜃=
ℎ
𝑝
 cos𝜃=
𝑏
ℎ
sec𝜃=
ℎ
𝑏
 tan𝜃=
𝑝
𝑏
cot𝜃=
𝑏
𝑝
20. GEOMETRY
 sum oftotal anglesofa polygon= (n-2)180
 so each angleofa polygon 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐
(𝒏−𝟐)𝟏𝟖𝟎
𝒏
Acumen:- the abilityto make goodjudgementsandtakequickdecisions,astuteness,shrewdness,
canniness,sagacity
21. Series
 Arithmetic Progression
 nth term Tn= a+(n-1)d
 sum ofn terms Sn=
𝒏
𝟐
[2a+(n-1)d]
 sum ofn continuoustermsstartingfrom 1=
𝒏(𝒏+𝟏)
𝟐
 Sum offirstn evennumbers= n(n+1)
 Sum offirstn oddnumbers= 𝒏 𝟐
22. Quadratic equation
If a𝒙 𝟐+b𝒙+c=0Then 𝒙 =
−𝒃±√ 𝒃 𝟐−𝟒𝒂𝒄
𝟐𝒂
23. MISCELLANEOUS
 (𝒂 + 𝒃) 𝟐 = 𝒂 𝟐+2ab+𝒃 𝟐
 𝒂 − 𝒃 𝟐=𝒂 𝟐-2ab+𝒃 𝟐
 (𝒂 + 𝒃) 𝟐= 𝒂 − 𝒃 𝟐+4ab
 (𝒂 − 𝒃) 𝟐 = (𝒂 + 𝒃) 𝟐-4ab
 𝒂 𝟐 − 𝒃 𝟐 = (a + b) (a-b)
 (𝒂 + 𝒃) 𝟑=𝒂 𝟑+𝒃 +3ab(a+ b)
 (𝒂 − 𝒃) 𝟑=𝒂 𝟑-𝒃 𝟑-3ab(a-b)
 𝒂 𝟑+𝒃 𝟑= (a+b)(𝒂 𝟐-ab+𝒃 𝟐)
 𝒂 𝟑-𝒃 𝟑=(a-b) (𝒂 𝟐+ab+𝒃 𝟐)
 (𝒂 + 𝒃 + 𝒄) 𝟐=𝒂 𝟐+𝒃 𝟐+𝒄 𝟐+2ab+2bc+2ca
 𝒂 𝟑+𝒃 𝟑+𝒄 𝟑-3abc=(a+b+c)(𝒂 𝟐+𝒃 𝟐+𝒄 𝟐-ab-bc-ca)
=
𝟏
𝟐
[a+b+c] [(𝒂 − 𝒃) 𝟐+(𝒃 − 𝒄) 𝟐+(𝒄 − 𝒂) 𝟐]

12. If a +b +c=0, Then 𝒂 𝟑+𝒃 𝟑+𝒄 𝟑=3abc
 If any numberwill fit inthe form of(6k+1)or(6k-1) then numberwill bea primenumber.
 ThedifferencebetweenC.I andS.I for2 yearsis
Diff=P(
𝑹
𝟏𝟎𝟎
)
𝟐
 Sum ofall exterioranglesofa polgon=360°
 So oneexteriorangleofpolygonofnside=(
𝟑𝟔𝟎
𝒏
)
 If n personare shakinghandwitheach otherin a groupthen
Total no. Of handshake=
𝒏(𝒏−𝟏)
𝟐
Juggernaut:-extremelylargeandpowerful,that cannotbe stopped,a hugepowerful and
overwhelmingforce