Prologue
In the Assistant Central Intelligence Officer (ACIO) exam, youâve to face two papers
 Paper I: 100 Multichoice questions from General Awareness + aptitude (=Maths + reasoning)
 Paper II: English Essay worth 50 marks
Total time limit: 1 hr 40 minutes
In this article, we see the approach for Maths, reasoning and English.
The approach for General awareness (History, geography, science, current affairs etc.) is given in a separate article: click me
In ACIO 2012 Question paper, the internal breakup was:
General Awareness  79 
Maths  9 
Reasoning  12 
Total MCQ  100 
Therefore, Maths+ Reasoning=9+12=21= approx. 1/5^{th} of paper was about Aptitude. So cost:benefit is quite good but Practice@home=essential, otherwise following things will happen:
#1: silly mistakes in calculation
wrong  right 
x5=(15/2)2*x5=152x=15+52x=20
x=10 
x5=15/22(x5)=152*x(2*5)=152x10=15
2x=25 x=12.5 
#2: formula problem
you wonât be able to recall formulas or you will plug wrong values in the formula=> either way answer will not come. (Example: area of equilateral triangle asked in ACIO2012)
#3: time problem
 In maths, Because of problem #1 + #2= your answer will not match the given options A/B/C/D then you recalculate the whole sum again=time wasted.
 In reasoning, youâll take lot of time in each sittingarrangement/bloodrelation / codingdecoding type question. = time wasted
In short, if you want to crack a government / Bank / PSU exam=> aptitude practice@home is essential.
Maths / Quantitative Aptitude
Donot Fear Maths, Donot Hate Maths. If you basic concepts are clear and you practice enough at home, then most of maths/reasoning questions can be solved without effort or mistake during the exam.
Negative thinking âmaths is too difficult, ye mujse nahi hogaâ=> youâll only dig your own grave while others prepare maths and get selected for the job.
For all competitive exams of India, we can classify math topics into following
Regular topics  SSC/CDS/CAT exclusive  Misc Topics* 
prepare for ACIO  Ignore for ACIO  prepare for ACIO 

(Usually nonSSC/CDS/CAT exam donât bother much asking questions from this topics). 
(Most govtjob exams nowadays donât bother with these topics but they were asked in ACIO2012 hence need to be prepared.) 
Preparation Source:
 NCERT maths (free download @bottom)
 Mrunal.org/aptitude
 Any one Quantitate Aptitude book. Even second hand /used copy will work you donât need latest edition. Based on their utility for SSCCGL exam, I classify the Quant books into 3 types:
will work in ACIO + Useful for SSCCGL; CDSBecause quadratic eq., trigonometry and geometrytheory (nonAVP) is covered properly.  
will work in ACIO but Not so useful for SSCCGL; CDSBecause quadratic eq., trigonometry and nonAVP geometry is not covered in length.  
Useless for any exam  Readymade Junk from jholachhap publishers like âACIO guide book; RBI assistant guidebook; National Insurance AO guidebookâ etc. 
 For additional practice you may go through previous SSC question papers (but ignore trigonometry, quadratic equation and geometry except Areavolumeperimeter.)
Permutation combination probability (PCP)
In the late90s, this used to be the hotfavorite topic for govt.exams, but nowadays rarely comes. However ACIO2012 did contain two questions from PCP (meaning ACIO papersetter uncleji still runs with 90s mindset) so youâve to prepare PCP. Most of the PCP stuff can be solved without any formulas. Go through following articles
 [Aptitude] Permutation Combination made easy without Formulas
 [Aptitude] Combination: Coins possible Sums (without formula)
 [Aptitude] PnC: arrange such that two people Always sitting together?
 [Aptitude] PnC: How many Ways to arrange letters of word “RECUPERATE” (Permutation without Formulas)
 [Aptitude] PnC Arrange digits in ascending order to form numbers (asked in UPSC 2009)
 [Aptitude] PnC: Conditional Selection in Committee
 [Aptitude] PnC: Binomial Expansion. How many ways to select one or more out of given Items?
Additionally, I had also uploaded a few shortlectures about PCP on youtube you can see them on:
http://www.youtube.com/user/TheMrunalPatel/videos?view=1&flow=list
And then solve maximum questions from your Quant book.
Observe the questions from 2012âs ACIO paper:
There is a 7digit telephone number with all different digits. If the digit at extreme right and extreme left are 5 and 6 respectively, find how many such telephone numbers are Possible.
 120
 1,00,000
 6720
 30,240
Seven digit phone number looks like this
6*****5
so weâve five empty seats, and weâve 8 gentlemen (0,1,2,3,4,7,8,9). Question demand âall different digitsâ so we canât use 5 or 6 again. so five seats and eight gentleman. Order/sequencing of number matters. (Because in phone number 1234 is different than phone number 4321). So this is a permutation problem.
= seat1 and seat 2 and âŚupto seat5
= _ x _ x _ x _ x _ (because in permutation/combination: âandâ means multiplication)
= first seat has 8 option x second seat has 7 options x third seat has 6 options..
=8 x 7 x 6 x 5 x 4
=6720 Answer C
Probability
Probability questions can also be solved with mere extension of Permutationcombination concept. Read the following articles
 [Aptitude] Probability Made Easy (Extension of Permutation Combination Concept!)
 [Aptitude] Probability : Two Dice problems Sums and multiples
And then solve maximum questions from your Quant book.
Observe the Question from ACIO 2012:
A speaks the truth 3 out of 4 time, and B speaks truth 5 out of 6 times . What is the probability that they will contradict each other in stating the same fact?
 2/3
 1/3
 5/6
 1/21
A speak true=3/4 that means chances of A telling lie =(1 3/4)=1/4
same way chances of B telling lie=1/6
In probability related question, convert the question into a Statement
Two people will contradict each other, when one speak truth and other is lying
=(A true AND B lie) OR (A lie AND B true)
but in probability, And=multiply (x) and OR=add(+) ;
=(3/4 x 1/6) + (1/4 x 5/6)
=3/24 + 5/24
=8/24
=1/3 answer is B
APGP
arithmetic progression  Basics of Arithmetic progression explained in NCERT Class 10 Chap 5. (free downloads @bottom) 
geometric progression  class 11âs NCERT chapter 9. 
Then practice sums from your quantbook. APGP does require memorizing a few formulas.
Observe the question from ACIO2012 Exam
After striking the floor, a ball rebounds to 4/5th of the height from which it has fallen, Find the total distance that if travels before coming to rest if it has been gently dropped from a height of 120 metres.
 540 meters
 960 meters
 1080 meters
 1120 meters
Ball dropping=geometric progression (GP).
Approach #1
The special readymade formula for ball dropping GP case is,
Distance=height x (1 plus rebounding ratio) / (1 minus rebounding ratio)
Distance
=120 x (1+4/5) / (14/5)
=1080 mts
Approach #2
Distance travelled by ball
=down + {up + down} + {up + down} +âŚ infinite (not infinite in reality though!)
=120 + {4/5(120) + 4/5(120)} + {4/5 [4/5(120)] + 4/5 [4/5(120)]}âŚupto infinite
=120 + 2 x 4/5(120) + 2 x 4/5 [4/5(120)]âŚ upto infinite
=120 + 2 x 120(4/5 + (4/5)^{2} + (4/5)^{3}âŚupto infinite)
but in such infinite GP series highlighted in bold, the summation formula is S=a /(1r)
therefore sum of bold part
=(4/5)/[1(4/5)]=4
=120 + (2 x 120 x 4)
=120 + (120 x 8)
=120 x 9
=1080 meters.
Now, Moving to the regular topics:
Basics (bodmas, surdsindices etc)
In the banking exams, usually first few questions have lengthy multiplication division etc. based on BODMAS. While you donât need that speedmaths ability for ACIO, but basics should be clear otherwise youâll make silly calculation mistakes in remaining topics.






Algebra, Linear Eq.
âMotherâs age was x and daughters age..â; â3 mangos and 5 bananas purchased forâŚâ ; X+1/2x+3=3/8 then find X.
^This type of stuff. Just practice and youâll get a hang of it.
 Basics given in NCERT Class 8 Chap 2 and 9.
 Then NCERT Class 9 Chap 4
 Lastly NCERT Class 10 Chap 3.
 them maximum practice from your quant book
letâs solve ACIO2012 question
A toy weighing 24 grams of an alloy of two metals is worth Rs 174/, but if the weights of the two metals be interchanged, the toy would be worth Rs 162/ If the price of one metal be Rs 8 per gram, find the price of the other metal used to make the toy
 Rs 10/ gram
 Rs 6/gram
 Rs 4/ gram
 Rs 5/gram
Suppose two metals: A and B. A costs 8 rupees and B costs âbâ rupees.
Situation #1
metal  price  wt  total price 
A  8  m  8m 
B  b  n  bn 
m+n=24 gm (total qty)  8m+bn=174âŚeq1 
Situation #2
Now we interchange the weights
metal  price  wt  total price 
A  8  n  8n 
B  b  m  bm 
m+n=24 gm (total qty)  8n+bm=162âŚeq2 
now weâve two equations
8m+bn=174
8n+bm=162
add left side to left side and right side to right side
(8m+bn)+ (8n+bm)=174+162
Rearrange
(8m+8n)+(bm+bn)=336
take â8â and âbâ common
8(m+n)+b(m+n)=336
but we know that total weight of new alloy is 24gms that means m+n=24
8 x 24 + b x 24=336
24 x (8+b)=336=> you get value of b=6
Ans. price of second metal is Rs.6 per gram
Average Allegation

Can be solved without formula. Go through https://mrunal.org/2012/03/aptitudealligationsmixturesalloys.html 

complex questions can be made even from simple average. click me to solve them without formulas 

For ratioproportion NCERT Class 8 Chap 13. 

https://mrunal.org/2012/05/aptitudepartnershipandprofitsharing.html 
Time speed distance work
This involves
 Time speed distance
 Trains, platforms
 Boatsstreams
 Time and Work
 Pipes and Cisterns
All of them can be solved with our universal STD formula. see following articles to learn the concept
 [Aptitude] TSD: Average Speed made easy without Formulas (Our Good olâ STDTable Method!)
 [Aptitude] TSD: Average speed question from CSAT2012
 [Aptitude] Pipes and Cistern problem: 3 pipes, 2 work together
 [Aptitude] STD Table: Two complex cases of Time and Work
 [Aptitude] Time n Work : P and Q start together but P leaves after some days
 [Aptitude] Boats and Streams madeeasy using our STDTable Method
 [Aptitude] TnW: How long did the Work last?
 [Aptitude] TnW: A is thrice as good as workman as B
 [Aptitude] Time n Work: 4 men and 6 women can complete a work in 8 Days then
 [Aptitude] Time n Work :Daily Wages and Share in Payment
Then solve max. questions from your quant book
letâs try the question asked in ACIO 2012
 A man decides to travel 80 kilometers in 8 hours partly by foot and partly on a bicycle. If his speed on foot is 8 km/hr and on bicycle 16 km/hr, what distance would he travel on foot?
 20 km
 30 km
 48 km
 60km
Suppose he walked for âtâ hours on foot. meaning he spent (8t) hours on bicycle. (because total time he took is 8 hrs)
Then make an STD table like this:
on foot  on bicycle  
speed(S)  8  16 
time(T)  t  8t 
distance(D) 
STD formula is: speed x time = distance
Apply it in both cases and fillup cells
on foot  on bicycle  
speed(S)  8  16 
time(T)  t  8t 
distance(D)  8 x t  16 x (8t) 
As per the question we know that total distance he covered was 80kms. Therefore
(distance covered on foot)+(on bicycle)=80
8t+16 (8t)=80
8t+ (16*8)16t=80
8t+ 16*8=80
when you solve this equation you get t=6 hrs. update the table
on foot  on bicycle  
speed(S)  8  16 
time(T)  6  8t 
distance(D)  8×6=48kms  16 (8t) 
Ans. He travelled 48 kms on foot.
Approach #2: Alligiation (Wine Water)
we can also solve this question using alligiation method. How?
first understand the concept explained in following article:
[Aptitude] Alligations,Mixtures,Alloys: Water,Milk,Wine mixing: Weighted Average
letâs check the same ACIO question again
A man decides to travel 80 kilometers in 8 hours partly by foot and partly on a bicycle. If his speed on foot is 8 km/hr and on bicycle 16 km/hr, what distance would he travel on foot?
Since he travelled 80kms n 8 hours, his average speed is
Speed x time = distance
Speed x 8 =80=> avg. speed = 80/8=10
Make the winewater table:
concentration (speed)  8 (foot)  10 (avg)  16 (cycle) 
volume (time)  t  (8t) 
Apply the visual move, you get two equations:
1610=t => t=6
108=(8t) =>t=6
In either case t=6
And the distance travelled on foot=> speed x time=8 x 6=48 kms our final answer.
for getting more grip: read following article
 [Aptitude] Product Consistency: If Sugar price increases then consumption should be Decreased by What %, TimeSpeedDistance problems,
 [Aptitude] Alligation: Advanced applications in Interest rates, Profitloss, Average Wages (WineWater Concept)
 [Aptitude] Time n Distance: Early and late to office (shortcut using product consistency method) for SSC, IBPS, CSAT, CAT, CMAT
Percentage, profitloss, SICI
All questions whether it is profitlossdiscountmarket price ; or simple / compound interest or population increase / decrease=>all of them can be solved without formulas, as long as your basic concept about % is clear. so first understand the concept from following articles
 [Aptitude] Concepts of Marked Price and Successive Discounts (ProfitLoss) without (stupid) formulas
 [Aptitude] Compound Interest Rate, Population Growth without Formulas
 [Aptitude] Alligation: Advanced applications in Interest rates, Profitloss, Average Wages (WineWater Concept)
 [Aptitude] Product Consistency: If Sugar price increases then consumption should be Decreased by What %, TimeSpeedDistance problems,
Now letâs try the ACIO 2012 question
Due to a 25 % increase in the price of rice per kilogram a person is able to purchase 20 kilograms less for Rupees 400. What is the increased price of rice per kilogram?
 Rs 5
 Rs 6
 Rs 10
 Rs 4
this question calls for âproduct consistencyâ approach
If rice price increase by 25% then consumption must decrease byâŚ20% (how? letâs see)
25% increase= new price is 125%=5/4
now just inverse it and subtract from 1
14/5=1/5
1/5=20%
That means If rice price increase by 25% then consumption must decrease byâŚ20%
But in the question theyâre saying âWhen rice price increased, customer could be 20kg lessâ
Meaning the decrease of 20kg=20% of the original qty.
Then what was the original qty of rice that customer could buy, before the price rise?
in this question, situation is simple: 20%=20kg then obviously 100%=100kg.
meaning customer was originally buying 100kg rice, for rupees 400. and now he can buy only 10020=80 kg for 400 rupees.
Therefore, new price of rice per kg =Rs.400/80kg=5 Rs.per kg.
Number theory, LCMHCF
topic  approach 


letâs check Questions from ACIO 2012
Three bells chime at intervals of 48, 60 and 90 minutes respectively. If all the three bells chime together at 10 AM, at what time will all the three chime again that day
 1 PM
 2 PM
 8 PM
 10 PM
This is an LCM question
LCM of (48,60,90)=720 (how to find LCM has been explained in above article)
Meaning theyâll ring after 720 minutes (but weâve to convert it into hours): 720/60=12hrs
If bells rang together @10AM then theyâll again ring after 12hrs. (Imagine wall clockâs hour hand moving)=after 12 hours the hour hand will again come @10 but itâll be night= 10PM answer is D
Finding last two digits
This was also asked in ACIO2012
 Find the last two digits of : 15x37x63x51x97x17
 35
 45
 55
 85
Make pairs of two number, just focus on last two digits.
15 x 37 =15(30+7)=150+105=last two digits 55
63 x 51=63 (50+1)=3150+63=last two digits 13
97×17=17(90+7)=1530+119=last two digits 49
Now weâve three new numbers: 55 x (13 x 49)
13 x 49=13 (40+9)=520+117=last two digits 37
now weâve two numbers
55 x 37 =55 (30+7)=1650 + 385=last two digits 35
Final answer: 35.
AVP (Area Volume Perimeter)
 Basics explained in NCERT Class 8 Chap 3, 11.Then NCERT Class 9 Chap 9, 12, 13.
 Lastly NCERT Class 10 Chap 13
 in your quant.book youâll find the consolidated list of formulas and demo questions.
Letâs check the question asked in ACIO2012
A circle is inscribed inside an equilateral triangle touching all the three sides, If the radius of the circle is 2 cm, find the area of the triangle.
 15 root 3
 18 root 3
 12 root 3
 12 root 2
In equilateral triangle, if you draw a median, then the center of incircle divides it in 2:1 ratio.=>total length is 3 parts.
Meaning 1 unit =>total length of median will be 1 x 3 =3 unit
We know that radius is 2cm. 2 unit=>total median length will be 2 x 3=>6 units (cm)
Then you run Pythagoras, you get side âaâ=(12 / root3)
And for equilateral triangles the area is=(root3)/4 x a^{2}
Plug in the value of âaâ and you get answer=12 root 3.
enough of maths, letâs move toâŚ
Reasoning
As per ACIO2012 paper, this portion punning more or less parallel to other exams minus nonverbal ability.
the Recommended Book is as usual: RS Aggarwalâs Modern Approach to verbal and nonverbal reasoning . Then the question is, how to prepare reasoning in systematic manner in the given time?
Do it in following way
#1: Chart based
 This includes: Direction sense test, Sitting arrangement (rectangle, circular, building, lecture schedules etc.) and blood relations.
 I club them together because in most of them youâve to make rough diagram / chart / table to solve it. prepare them in following order:
Sr.No  Topic  RS Aggarwal Chapter No. 
1.  Direction Sense Test.  8 
2.  Sitting arrangement: circular  6 
3.  Sitting arrangement: rectangle  6 
4.  Sitting arrangement: âtableâ based e.g. lecture schedules, jobcarcloth color, buildingcarnewspaper etc.  6 
5.  Blood relations  5,6 
6  Number ranking time sequence  12 
7  arithmetic reasoning  15 
#2: coding n series + alphabet
Sr.No  Topic  RS Aggarwal Chapter No. 
1.  Codingdecoding  4 
2  alphabet tests  10 
3.  Alphanumeric sequence puzzle  11 
#3 Analogy, odd man
Sr.No  Topic  RS Aggarwal Chapter No. 
1.  Analogy  2 
2.  Oddmen out  3 (chapter title is âClassificationâ) 
Nonpriority
After youâre done with above topics, if time permits, do following ânonpriorityâ things from RS Agarwalâs
topic  chapter in RS Aggarwalâs reasoning book 
Input Output  7 
Logical venn diagrams  9 
Mathematical operations  13 
logical sequence of words  14 
insert missing characters  16 
Data sufficiency  17 
Eligibility tests  18 
situationreaction, assertionreasoning, verification of truth  19 to 21. 
logical deduction (syllogism etc)  section II of his book 
nonverbal  end part of his book 
Reasoning questions asked in ACIO 2012
coding decoding  coding decoding 


sitting arrangement  blood relations 


DBT (Direction Based Test)  Puzzle Test 


calendar  sequenceseries 
1. If it was Saturday on 17th December, 1982 what will be the day on 22nd December, 1984(i) Monday(ii)Tuesday(iii) Wednesday
(iv) Sunday 
1. One term in the following number series is not correct. 15, 16, 22, 29, 45, 70 Find out the wrong term?(i) 16(ii) 22(iii) 45
(iv) 70 
English
Unlike SSC/IBPS/LIC/CAPF/CDS, here you donât have to face any grammar, comprehension, vocabulary, idioms or phrases. You just need to write one essay worth 50 marks.
Copy pasting the ACIO2012 Question paper
Write an essay in English language in only on any one of the following topics is not more than 400 words. (50 marks)
 Indiaâs Space Programme
 Causes of corruption in India
 How to deal with left wing extremism.
 Depending on your fontsize/handwriting, 400 words meaning ~45 pages (singleside).
 To write a decent essay, what you need is decent points. Essay can be on variety of topics, so ideally you need to keep reading newspapers, magazines, and some good books from library on regular basis. After some months, you have good points on almost every topic.
However: given that not many weeks are left before the ACIO exam what to do for Essay?
@the bottom of this article, Iâve given two things
 IGNOU India democracy and Development zip file. This PDF set contains lot of fodder points to approach most of the social/democracy/Development etc. topics related essays.
 Topic wise Huge list of essays, from previous UPSC, LIC etc exams.
Fundamental principles remain same like UPSC Essay: spend the first few minutes on brainstorming the idea. Then rank those ideas, start writing essay: introduction >> body (+/ pros, cons) >> conclusion. (click me for more on Essay tips)
Then every day, you try to solve a few essays in your head: Brainstorm for the idea, what will I write in this essay? Can I write 400 words or not if not then dig books/google for the content.
Also write a few essays on your own every week. (If you donât have writing practice, then you wonât be able to maintain speed doing the actual exam)
there is no dearth of readymade essay books in the market, but that type of firefighting/desi jugaad, I donât find it very helpful because such books are either outdated (only reprinted, not updated after 90s), and or donât cover all the necessary topics. But still, if you want to refer to any books, you may use Spectrum Book of Essays or if you have anyother book that is also fine. You donât have to reproduce the same essay verbatim from those books, you can write the essay in your own words but try to avoid silly grammar/spelling mistakes, write as neatly as possible, without any scratches.
Appendix: Download
NCERT Mathematics
Mathematics Class 8  Download 
Mathematics Class 9  Download 
Mathematics Class 10  Download 
Mathematics Class 11 (Only AP, GP)  Download 
Essay writing

Click Me 

Click Me 
The strategy/approach for GA/GK portion of ACIO exam is given in a separate article click me
131 Comments on “[Studyplan] ACIO: Aptitude, Maths, Reasoning and English Essay for Assistant Central Intelligence Officer (ACIO) exam”
marvellous job… Mrunal sir
sir please suggest the essay topics for 2014 acio exam .that will helpful for us…
hi sir .Can u keep some essay topics on ib acio plz sir thank uuuu
ACIO Admit Cards released.
Please post some expected essay for acio exam 2015
great work..thanks a lot sir
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How to study general awareness for acio?