AptitudeAnalysis
 Questions not too difficult. Still, if you couldn’t solve all 20 questions accurately, it means (1) you didn’t know the concept/formula/theory (2) you made silly mistake in multiplication/division/addition or subtraction. You can make all excuses about engineer/nonengineer, sci/nonscience. But in the end, competition world is cruel, so you’ve to increase practice. The one who runs away from aptitude, usually ends up digging his own grave.
 Like last year, they again asked 20 questions from aptitude. Hence weightage/importance of Aptitude hasn’t changed for UPSC CAPF exam.
 Last year the pattern was: 13 reasoning and 7 (maths+DI). This year, pattern has reversed: 13 (maths+DI) and 7 reasoning
 Like last year, one question on pie chart
 Like last year, one question on dice position.
 Like last year, one question on clock
 unlike last year: no questions from direction sense test or assumption inference.
 like SSC CGL, UPSC has also found new attraction for Geometry. Out of 10 maths questions, 4 came from geometry.
AptitudeInternal breakup
Solved with help of Mr.Deepak Singh and Mr.Manu Jha.
Maths  profit loss  1 
basic numeracy/algebra  2  
Geometry  4  
ratioproportion  1  
timespeeddistancework  2  
maths subtotal  10  
DI  Data interpretation  3 
Reasoning  sequenceseries  1 
codingdecoding  2  
logical venn diagram  1  
clockcalendar  1  
NonVerbal  2  
reasoning subtotal  7  
total  overall  20 
Correction / if you know even faster methods, do share in comments
overall
Polity  14  Covered. Click me 
Geography+EnB+Agro  14+8  Covered. Click me 
Economy+IR+PIN  21+4+2  Covered. Click me 
Science  20  Click me for Answerkey 
History  22  click me 
Aptitude  20  Given here 
total  125 
Maths
Profit Loss
Q1. selling an article @270, a man loses 10%. If he would sell it @360, his gain percentage is?
 10
 15
 20
 25
He sold @10% lost=90% of cost price, meaning 270 =90% of cost price. Therefore cost price=270/0.9=Rs.300
His cost price is 300 and if he sells at 360 then profit percentage?
=[(360300)/300] x 100=60/3=20% answer (C)
Alternatively: 360/(270/0.9) =1.20=>100+20 hence profit is 20%
Basic numeracy/algebra
Q1. 9 mangoes cost as much as 5 oranges. 5 oranges cost as much as 3 apples. 4 apples as much as 9 pineapples and if 3 pineapples cost 48. what will a mango cost?
 9
 12
 18
 27
Start from reverse: 3 pineapples = 48 meaning 1 pineapple =48/3=16 Rs.
given  meaning 
4 apple=9 pine  1 apple=9P/4 
5 orange=3apples  1 orange=3A/5=3*9*P/(5*4)=27P/20 
9 Mangoes=5 oranges  1 mango=5*orange/9=5*27P/(20*9) 
but we know that 1 pineapple=16, so,
1 Mango=5*27(16)/(20*9)=>12 Rs. Answer B
Method 2
9 mangoes = 5 oranges =3 apples… (1)
4 apples = 9 pineapples …(2)
3 pineapples = Rs. 48 => 9 pineapples = 48 *3 => 4 apples = 48 *3 (from 2)
1 apple = 12*3 => 3 apples =12*3*3 => 9 mangoes = 12*3*3 ( from 1)
Therefore, 1 mango = Rs. 12 .. option (b)
Method 3
Every fruit’s 1st Alphabet has been taken as variable.
 9M = 5O = 3 A
 4A=9PA
 3PA =Rs 48
 1PA = Rs16
 9PA = Rs144
 4A=Rs 144
 3A=Rs 108
 9M=Rs 108
 1M =Rs12 hence answer (B)
Q2. least integer whose multiplication with 588 leads to perfect square is?
 2
 3
 4
 7
Factors of 588 = 2*2*3*7*7
we already have pairs of twos and pairs of seven. Only three is alone. Hence to make a perfect square, we need to multiply it with 3 =>answer (B)
Ratio
Q1. if the ratio of X:Y=3/4 and ratio of Y:Z=12/13 then ratio of X:Z is
 13/3
 1/3
 4/13
 9/13
Method 1
 Method 2

TimeSpeedDistanceWork
Q1. If 5 persons can weave 180 mats in 8 days, how many mats can 8 persons weave in 6 days?
 200
 192
 190
 180
Suppose speed of one man is “m”.
situation A  situation B  
Speed (S)  5m  8m 
time (T)  8  6 
distance (D)=speed x time  160=5m*8  D=8m*6 
Since speed x time = distance.
5m x 8=160=>m=4.
Replace this value in column B’s distance=8m x 6= 8*4*6=192 mats. Answer (B)
Q2. Two cars are moving in the same direction with a speed of 45 km/hr and a distance of 10 km separates them. If a car coming from the opposite direction meets these two cars at an interval of 6 minutes, its speed would be:
 45
 55
 65
 75
Method1: Train concept
Assume the two cars=first and last wagon of one big train. This train is 10km long!
And with respect to this train’s width, the third car is merely a ‘dot’=assume it is a motor cycle.
Rephrasing the question now:
A train of 10km length is moving at a speed of 45kmph. A motorcycle from opposite direction crosses this train in 6 minutes. What is the speed of that motorcycle?
SPEED  since opposite direction = have to add speeds. Hencefinal speed (S)=speed of train + speed of motorcycle=(45+m) 
TIME  time taken to finish distance(T)=6 minutes=6/60 hours. 
DISTANCE  Distance=10 kms (the length of train). 
apply the STD formula
speed x time = distance
(45+m)*(6/60)=10
m=55 kmph answer (B)
Method #2
 Car coming from opposite direction meets first car, after 6 minutes it meets second car.
 In that 6 minutes first car has covered 4.5 km
 As D=s*t = 45 *6/60= 4.5 km
 Remaining 5.5 km(104.5 = 5.5) covered by car coming from opposite direction in 6 minutes. Let it’s speed be x km.
 Therefore, 5.5 = x * 6/60 => x = 55 km/hr..option (b)
Geometry
Q1. find area of the shaded portion
 164pie
 16pie
 4pie
 42pie
Observe the smaller square highlighted in purple color.
Size of that smaller square in purple region=one fourth of the big square.
Size of the pie in that purple region=one fourth of the large circle.
therefore, size of the shaded portion
=[small square minus small pie]
=[1/4 (area of big square) minus 1/4 (area of big circle]
=1/4[4^{2}pie*2^{2}] ; important: the diameter of big circle=4 hence radius=2.
=1/4[164pie]
=[4pie]
Hence answer (C)
Q2. Sum of the base and altitude of a triangle is 30cm. What is the maximum possible area of such triangle?
 100
 110
 112.5
 120
Area of triangle= 1/2x (base x altitude)
hence area will be maximum when base=altitude
since base + altitude=30cm so for both of them to be equal they’ve to be 15cm each.
Now for a triangle with b=15cm and h=15cm, the area will be
=1/2 x b x h
=1/2 x (15 x 15)
=112.5 hence answer C
Q3. person walks from O to circular path AB, as shown by arrows. If radius=100 meters then what is the total distance walked (approximately)
 703
 723
 743
 823
The circular path
total degrees=360
he is walking a circle of 36060 degrees=300 degree.
the circumference of an Arc with 300 degrees
=(300/360)*2pie*radius….eq1
The triangle path
He is walking (OA+OB)…eq2
total distance covered
=eq1+eq2
=(300/360)*2pie*radius+(OA+OB)
=(300/360)*2*3.14*100+(100+100)
=723.33
Hence C is the answer.
Q4. in the following triangle, what is the value of X?
 51
 360/7
 62:6/7
 49:4/7
Since 4y is an exterior angle hence
4y=x+2y.
x=2y…eq1
And in a triangle, sum of three angles=180 so,
A+B+C=180
x+2y+3y=180
x+5y=180
2y+5y=180 (from eq1 we know x=2y)
7y=180
y=180/7
plug this value back in eq1
x=2y
x=2*180/7=360/7 hence answer (B)
Data interpretation
Q1. A campus poll covering 300 undergraduate students was conducted in order to study the students’ attitude towards a proposed change in rules for hostel accommodation. The students were required to respond as ‘support’, ‘neutral’ or ‘oppose’ with regard to the issue. Find number for support, neutral and oppose respectively
 150,90,60
 120,100,80
 80,100,120
 60,90,150
shortcut
A circle has total 360 degrees, out of them 96 degrees oppose.
Think in this way – if 96/360 oppose then how many in 300 student oppose?
96/360=Opp/300=>opp=96*300/360=80 students oppose.
So, in the answer (support, neu, opp)= (support,neu,80)
There is only one such pattern given in Option B. Hence answer B
longcut
so far we found oppose=80. continue finding others
support=144*300/360=120
and finally neutral=total students MINUS (support+oppose)
neutral=300(80+120)=100
therefore, (support, neu, opp)=120, 100, 80. hence answer (B)
Q2. Expenditure of two families
expense  family A  family B 
Misc  20%  70% 
Entertainment  30%  20% 
Food  50%  10% 
Monthly Income Rs  20,000  1 lakh 
Correct statement
 Family A spends as much on misc. as family B spends on entertainment
 The food expense of family B is equal to the total expense of family A
 Family A and B spend equally on food
 Family A and B spend equally on entertainment
It’ll be better if we just convert percentages into absolute rupees.
expense  family A  family B 
Misc  20%=1/5^{th} of 20k=4k  70%=70k 
Entertainment  30%=3/10^{th} of 20k= 6k  20%=20k 
Food  50%=half of 20k=10k  10%=10k 
total income  20,000  1 lakh 
now check the statements
 wrong 
 wrong 
 Correct. 
 wrong 
Hence answer (C)
Q3.In a class,40 students passed in Mathematics, 50% of the students passed in English, 5% of the students failed in Mathematics and English, and 25% of the students passed in both the subjects. What is the ratio of the Number of students passed in English to number of student passed in maths?
 1:1
 2:3
 5:7
 10:9
Total students=40
Failed in both=5% of 40=2=> n=2
passed in both=25% of 40=10
passed in English=50% of 40=20
Construct Venn diagram
Those passed only in English=2010=10 students.
What about those passed only in maths?
=total MINUS (passed only in English + passed in both + failed in Both)
=40(10+10+2)
=18
so how many passed in MAths?
=passed only in MAths (but failed in English) + passed in both subjects
=18+10=28
Ratio: passed in English : passed in Maths=20:28=5:7. Answer (C)
Reasoning
SequenceSeries
Q1. Find the fifth term in this series: BCYX, EFVU, HISR, KLPO
 NOML
 NOLM
 ONML
 ONLM
Pattern: each term is made of two blocks, observe
BCYX  BC (move forward by one alphabet)=+D=EFYX (move backward by one alphabet)=W=UV and flip it=VU  result is second term EFVU 
On the same pattern
KLPO
KL + move forward by one alphabet (M)=NO
PO+ move backward by one alphabet (N)=LM and flip it=ML
Hence fifth term will be NOML=>answer (A)
Coding decoding
Q1. In a certain code, ‘PLANT’ is written as $@2*c and Yield is written as b64@%. What is the code for Delay?
 b4*2%
 b4@2%
 %42@b
 %4@2b
P  L  A  N  T 
$  @  2  *  c 
and
Y  I  E  L  D 
b  6  4  @  % 
plug in the values for Delay, using above chart.
D  E  L  A  Y 
%  4  @  2  b 
Hence answer (D)
Q2. A is coded as 1, B as 3, C as 5 and so on. Which of the following is the numerical value of the word ‘FAZED’ if the numerical value of CABLE is 41?
 81
 80
 79
 77
A= 1 , B= 3 , C = 5.
It is an Arithmetic progression with common difference 2.
hence pattern is a+(n1)*d
let’s make table only for the alphabets we need
A  1 
B  3 
C  5 
D  7 
E  9 
F  11 
L  12^{th} term=1+(121)*2=23 
Z  26^{th} term=1+(261)*2=51 
now let’s check
CABLE
=C+A+B+L+E
=5+1+3+23+9=41 (correct match to question condition.)
now FAZED
=F+A+Z+E+D
=11+1+51+9+7=79 hence answer (C)
Logical Venn Diagram
Q1. Which one among the following diagrams illustrates relationship among animals, cows and horses?
Animals (cows, horses).. option (c)
ClockCalendar
Q1. through how many degrees does the hour hand in a clock move as the time changes from 3 hours and 12 minutes to 6 hours?
 105
 99
 90
 84
shortcut
Hour hand is the shorter hand. If it moved from 3PM to 6PM, we can say 90 degrees. Hence at 3.12 minutes to 6PM, it’ll be less than 90 degrees. There is only one option (D) qualifies under this condition, because 84 is less than 90.
Longcut#1 (using hour distance)
Circle has total 360 degrees and a clock has markings for total 12 hours. Therefore, one hour=360/12=30 degrees.
approach 1  approach 2 
now the distance between 3:12 and 6=eq1 minus eq2=18096=84 degrees. Option D 

Longcut#2 (using minute distance)
 in a clock, 3 hours=90 degree and 3 hour=3 x 60 minutes=180 minutes
 therefore, 180 minutes=90 degree=>1 minute =90/180=0.5degree.
 from 3.12PM to 6PM, total minutes are 2 hours + 48 minutes=168 min (from 3 hr 12 mins to 6 hrs = 180 – 12 mins) 168 min = how many degrees ? 168*0.5=84 degree. Hence answer (D)
NonVerbal
Q1. what will be the next figure in this series?
Black dot is moving from corner to corner. Plus sign and white dot are moving cross to and fro. Whenever two signs coincide it becomes black dot. ..option (a)
Q2. Which one among the following boxes is similar to the box formed from the given sheet of paper (X)?
method1
F & B cant be adjacent sides. A ruled out.
D & A cant be adjacent sides. D ruled out.
E & C are opposite sides , Hence C ruled out.
Hence we’re left with answer (B)
method2
Visualizing the box B,E,F,C are on the same straight line and A,D forms the opposite sides of visualized box. Therefore one possible combination with respective opposite faces is
B <>F, E<>C , A<>D=option (b)
Correction / if you know even faster methods, do share in comments
Courtesy: Mr.Deepak Singh and Mr.Manu Jha for providing valuable inputs.
57 Comments on “[Answerkey] CAPF2013: Aptitude, Maths, Reasoning, Data interpretation solved with explanation”
Geometry qs no.3 answer is B i.e 723, you solved correctly but answer kept as C.
this is right
Sir for q3 right answer is B. You solved it right 723 is right but its B you marked it C
My lord mere saathi vakil sahi keh rahe hain… :P :P
answer of figurre qstns should b option B
Exactly. The small circle should not appear in figure..It is the correct answer.(B)
sir all my comments are not shown…….i cant figure reason why………nothing bad is written in them……?
Sir, i cant understand from where 160 came in the question
Time Speed – distance – work.
pls tell.
what will be the next figure in this series?
I think answer should be B. Bt not able to perfectly justify it!!
Yes, the right answer to the nextfigure? question is option B. I can justify it also :)
sir,
The venn diagram question:
They not mentioned 40 as total students but they are who passed in maths.
That’s the reason I was not able to find answer in exam hall.
please clear my doubt
Exactly…
This value is not required to answer the given question…. Just to confuse… If absolute value have been asked this value could have been helpful…
To a certain extend I agree with you.
But it seems 40 is number of students passed in Maths not total. When we solve percentage of students passed in Maths, it comes out to be 70%.
So, total number of students = 40*(100/70)= 57.1428. In fraction? How is it possible?
Giving value to confuse us is fine, but is should be consistent with the solution.
I may have calculated wrong or interpreted question wrong. So, you also check it :)
POINT Ravi…
But you have to mark one option and it is the closest… and upsc may give the argument that these percentages are approximated to nearest decimal which is I suppose a valid argument….
For Answer figure question, my logic is Black dot moves from corner to corner and plus and bubble to opposite corners. Plus or bubble has to disappear for a block once it has changed its position and reappear in the same position in the next block. Assume bubble had already changed its position in the first block. The option in this case would be B.
Q3.In a class,40 students passed in Mathematics ….and you have taken total no of student as 40….If u go by the wordings of the question then I don’t think one will be able to solve the problem…It might be that your interpretation is right but the way question has been put it is questionable.
For venn diagram qs, 25% only english, 25% both english and maths, 45 % only maths, 5 % not any one. So required ratio is english(50%) and maths(70%) so 5:7 answer is correct. We need not to find no of students.need not to consider statement i.e 40 students passed in maths.
last year the cut off for p1 was 97 and p2 it was 60. In my assumption this year the cut off for p1 is going to be 70 and p2 will remain same! what u guys think ?
I am getting approximately 145 in p1 and expect to get around 80 – 90 marks in p2 :)
Q3. Answer should be 5:7. The total no. of students is not 40 a/c to question. However, we don’t require the numerical value to determine the ration, as pointed by “PB” above. The value was misleading and those who could not solve it despite knowing the approach came in the trap of “40”.
*Q3 (DI)
Q3.In a class,40 students passed in Mathematics, 50% of the students passed in English, 5% of the students failed in Mathematics and English, and 25% of the students passed in both the subjects. What is the ratio of the Number of students passed in English to number of student passed in maths?
You have solved this question with the assumption that there are 40 students in the class which is not correct according to the question.
My Solution:
Let total no. of students: X
Pass in maths: 40
Pass in English: X/2
Pass in both: X/4
Hence, (X/2) + 40 (X/4) = X ==> can be verified by Venn diagram
=> X = 160/3 (although absurd as not possible to have students in decimal)
Anyways moving ahead:
Pass in English: (160/3) / 2
Ratio: 2:3
Correct me for anything wrong..
Question does not mention “passed in English only”.
50% should include 25% passed in both, isn’t it? If so,
Solution: Let the total no. of students be x.
Failed in both 5x/100.
Passed in one or more subject(s) 95x/100
Passed in both 25x/100
Passed in English only: 50x/10025x/100
Total students passed in Maths: {95(5025)}
Ratio of the Number of students passed in English to number of student passed in Maths: 50/70=5:7
Corrections, Please!
Now comes the absurd part: No. of students passed in Maths is 40. Total students = 40*100/70 = 57.14 not a natural number!!
*{95(5025)}x/100
Typo…
It is not asked in question to find the ratio of students only passed in English to those of Maths.
There was some problem in my solution:
My New Solution:
Let total no. of students: X
Pass in maths: 40
Pass in English: X/2
Pass in both: X/4
Hence, (X/2) + 40 (X/4) = (95/100)*X ==> As only 95% percent passed in atleast one subject
=> X = 400/7 (again absurd)
Anyways moving ahead:
Pass in English: (400/7) / 2
Ratio: (400/14) : 40 = 5:7
Lets hope UPSC gives number to all as having absurd total number of students :)
What about that 5% who failed in both????
Mrunal’s answer is correct because its a question of ratio which doesn’t depend upon the absolute value.
Even if we assume any other number we will get the correct ratio.
Here’s the proof:
Total students = 100
Failed in both=5% of 100 = 5 => n=5
passed in both=25% of 100 = 25
passed in English=50% of 100 = 50
Those passed only in English = 50 – 25 = 25 students.
What about those passed only in maths?
=total MINUS (passed only in English + passed in both + failed in Both)
= 100(25+25+5)
= 45
so how many passed in MAths?
=passed only in MAths (but failed in English) + passed in both subjects
=45+25 = 70
Ratio: passed in English : passed in Maths = 50:70 = 5:7. Answer (C)
you didn’t mention those 5% students who failed in both subject in you solution
plz clearify about the figure question and the electronic meters are still analog in india
let the total number of stu X
pass in math (only+both)= 40
pass in eng (only+both)= x/2
overall pass= 95% of x = 40x/4+X/4+X/2X/4
=> X= 40*20/9
THEREFORE,
PASS IN ENG = 40*20/9*2= MATH*10/9 => ENG/MATH= 10/9
*{95(5025)}x/100
Typo…
Q3.In a class,40 students passed in Mathematics, 50% of the students passed in English, 5% of the students failed in Mathematics and English, and 25% of the students passed in both the subjects. What is the ratio of the Number of students passed in English to number of student passed in maths?
its a wrong question.
*Q3 (DI)
Answer should be 5:7. The total no. of students is not 40 a/c to question. However, we don’t require the numerical value to determine the ration, as pointed by “PB” above. The value was misleading and those who could not solve it despite knowing the approach probably came in the trap of “40″.
Question does not mention “passed in English only”.
50% should include 25% passed in both, isn’t it? If so,
Solution: Let the total no. of students be x.
Failed in both 5x/100.
Passed in one or more subject(s) 95x/100
Passed in both 25x/100
Passed in English only: 50x/10025x/100
Total students passed in Maths: {95(5025)}
Ratio of the Number of students passed in English to number of student passed in Maths: 50/70=5:7
Corrections, Please!
Now comes the absurd part: No. of students passed in Maths is 40. Total students = 40*100/70 = 57.14 not a natural number!!
Dear Sir,
TimeSpeedDistanceWork
Q1. If 5 persons can weave 180 mats in 8 days, how many mats can 8 persons weave in 6 days?
5 person in 8 days =180 mats
so 1 person in 1 days = 180/(5*8)
= 4.5
so 8 person in 6 days = 4.5*8*6
= 216 mats.
but 216 not in the choice.
So I think question not correct; instead of 5 person 180 mats 8 days it should be “160” mats in 8 days
If 5 person can weave 160 mats in 8 days…then only 8 persons can wave 192 mats in 6 days…
Sir plz check this…….
Mrunal has taken 160 mats for calculation though question mentions 180 mats. Pls check !!
As per my calculation 192 will be answer for 160 mats and 216 will be answer for 180 mats.
Please check NONVerbal Q.1 box figure question ..
Answer should be B not A.
please explain it
For Answer figure question, my logic is Black dot moves from corner to corner and plus and bubble to opposite corners. Plus or bubble has to disappear for a block once it has changed its position and reappear in the same position in the next block. Assume bubble had already changed its position in the first block. The option in this case would be B.
i respect ur views but mrunal sir’s logic is more accurate…even i marked b:(
The position of + and . is exactly the same in both the cases.. Here the small circle should not appear as per the continuum of the question.
Sir! In Q3 of data interpretation , total no of students is not 40….40 students are passed in Mathematics..
Woohoo, I did all the 20 questions correctly!!!
The right answer to the nextfigure? question is option B, though.
The dice question can be solved by tearing the dice from Hindi side and folding it to visualise the answer
any guess about cut off mark for cpf ac 213
arnd 160 fr general category
155 obc
150 sc
145 st
Around 8590
IN THIS SECTION I ANSWERED 18 QUESTION AND ALL IS CORRECT.
THANX MRUNAL SIR .
Q1. selling an article @270, a man loses 10%. If he would sell it @360, his gain percentage is?
shortest way: (100loss%)/1st selling price= (100+gain %)/2nd selling price. ==> 90/270=100+gain%/360==>gain %=20 %%. solved in 20 seconds
A bird perched at the top of 12m high tree sees a centipede moving towards the base of tree from a distance equal to twice the height of the tree. The bird flies along the straight line to catch the centipede. If both move at the same speed, at what distance from the base of the tree will the centipede pick up by the bird?
the clock question:
i think the answer must be 105.
the angle must be calculated from 3:12pm to 6pm; from 3:15pm to 6pm its 90*, from 3:12 to 6 it must be 108 if not then, it can not be less than 90.
nope, sorry that was for minute hand, ignore my comment
but i can’t understand the dots question, what happens to the + mark ?
Sir, i cant understand from where 160 came in the question
Time Speed – distance – work.
pls tell.
M1*D1/W1=M2*D2/W2
5*8/160 =8*6/x
x=192
q3.
ans Let no of std be X
AQ: X40=50%OF X
X=80
Therefore total no is 80
now
Student passed in maths (40 given)
students passed in English 40. (50% of X)
so ratio is 1:1
Brother it misplacing in mat . in question there is 180
And in solutions. It’s 160
So that correct as per answer given is 192
So 160 is correct
In a class consisting of 100 students 20 know English and 20 do not know Hindi and 10 know neither English nor Hindi. The number of students knowing both Hindi and English is