Important Questions & Answers for Day-1 Campus Drive by · • 1. sum of ages are same. 2. also, its been said dat jim is dorthy's brother so jim kan be wid virginia or jane. 3. but

Important Questions & Answers for Day-1 Campus Drive

by

Ashwani Joshi

Associate Professor

Department of Electrical Engineering

Practice Sets on CT Compiled By: Prof. Ashwani Joshi Department of Electrical Engineering

Q. 1A bird keeper has got P pigeon, M mynas and S sparrows. The

keeper goes for lunch leaving his assistant to watch the birds. Suppose

p=10, m=5, s=8.

a.) When the bird keeper comes back, the assistant informs that x birds

have escaped. The bird keeper exclaims oh no! all my sparrows are

gone. How many birds flew away.

b.) when the bird keeper come back, the assistant told him that x birds

have escaped. The keeper realised that atleast 2 sparrows have

escaped. What is minimum no of birds that can escape.


Answer

A) 8 B) 15 + 2 = 17 ESCAPED


Q.2Three boys and three girls brought up together. Jim,

Jane, Tom, Virgina, Dorthy, XXX. They marry among

themselves to form three couples. Conditions are:-

i) Sum of their ages would be the same. ii) Virgina was the oldest. iii) Jim was dorthy's brother. iv) Sum of ages Jane+Jim and Tom+dorthy is

same. Give the three couples.


• Male------- JIM, JANE, TOM

Female--------- VIRGINA, DORTHY, XXX

................................................................so ......................

Jim is brother of Dorthy so jim having two options either Virgina or XXX.

But given that.... Virgina is oldest means she has to make couple with youngest Man and also

given that ages of Jane + Jin = Tom + Dorthy. So Tom is youngest man b/w them.

then couples are............

Tom - Virgina

Jin - xxx Jane

- Dorthy


• 1. sum of ages are same.

2. also, its been said dat jim is dorthy's brother so jim

kan be wid virginia or jane.

3. but see the 4th condition which clearly states dat sum

of ages of jim,jane and tom,dorthy are same.

Thus, jim,jane

tom,dorthy

xxx,virginia are the respective couples.


Q.3 If the digits of my present age are reversed

then i get the age of my son.If 1 year ago my age

was twice as that of my son.Find my present age


Answer

• My age : 10x+y and Son age : 10y+x

• so 10x+y = 10y+x • 10x+y-1 = 2(10y+x-1)

• x = (19y-1)/8

• for y=3 ; (19y-1) is divisible by 8

• Therefore x = 7 • So my present age : 10*7+3 = 73

• son's age : 10*3+7 = 37

Practice Sets on CT Compiled By: Prof. Ashwani Joshi


Q:4There are 6561 balls out of them 1 is heavy.

Find the min. no. of times the balls have to be

weighed for finding out the heavy ball.


Answer

• 7 times. • 6561 = 3 ** 8 • First, divide the group of 6561 into 3 groups of 2187. Take two arbitrary groups and

weigh them. Either they will be imbalanced (in which case you've identified the

group with the heaviest ball), or they are equal, in which case you know the 3rd

group has the heaviest ball. Split the heaviest group of 2187 into 3 groups of 729,

and continue on - so first test 6561, then 2187, then 729, then 243, then 81, then 9,

then 3 balls remain. You can deduce which one is heaviest at this (7th) step in

which 3 balls remain.


Q.5 If i walk with 30 miles/hr i reach 1 hour before and

if i walk with 20 miles/hr i reach 1 hour late.Find the

distance between 2 points and the exact time of reaching

destination is 11 am then find the speed with which it

walks.


Answer

• Let the time taken to travel with 30 miles/hr be x(1hour early) • Then time taken to travel by 20 miles/hr = x+2(1hour late) • Since the distance traveled with both the speed are same • 30 * x = 20 * (x+2) i.e 30 * x = 20 * x + 40 • 10 * x = 40 i.e x = 4(this is the time taken to travel with 30 miles/hr speed) • Now we know the time taken,Then Distance = speed * time taken i.e 30 * 4 = 120 miles. • To determine speed by which the person has to travel to reach the destination at 11.00 A.M simply

divide the distance(found out) by time taken.Here time taken is either one more than time taken

for 30 mile/hr travel or one less than • 20 miles/hr travel . time taken = 5 hrs (4+1 or 6-1) • speed = distance/time taken i.e 120/5 = 25 mile/hour.


Q.6On the Island of imperfection there is a special road, Logic Lane, on which the houses are

usually reserved for the more mathematical inhabitants. Add, Divide and Even live in three

different houses on this road (which has houses numbered from 1-50). One of them is a member

of the Pukka Tribe, who always tell the truth; Another is a member of the Wotta Tribe, who

never tell the truth; and the third is a member of the Shalla Tribe, who make statements which

are alternately true and false, or false and true. They make statements as follows:-

ADD : 1. The number of my house is greater than that of Divide's.

2. My number is divisible by 4. 3. Even's number differs by 13 from that of one of the

others. DIVIDE : 1. Add's number is divisible by 12. 2. My number is 37. 3. Even's number is even. EVEN : 1. No one's number is divisible by 10. 2. My number is 30. 3. Add's number is divisible by 3.


Answer (Not sure)

• add is living in 48 number(pukka tribe)

divide is living in 37 number(shalla tribe)

even is living in 30 number(wotta tribe)


Q.7 A family I know has several children. Each

boy in this family has as many sisters as brothers

but each girl has twice as many brothers as

sisters. How many brothers and sisters are there?


Answer

• answer:4 brothers and 3 sisters

let no. of girls=g n boys=b

b=g+1 ..........(i) as each boy have equal no. of sisters and

brothers and he is not included in brothers.so,1 is for him in g+1.

now ,

b=2(g-1)........(ii) as each girl have g-1 sisters.

solving (i) and(ii) we get g=3 and b=4


Q.8If A,B,C,D,E r 5 members of a family.4 of them

give true statements :

1. E is my mother in law 2. C is my son in law's brother 3. B is my father's brother 4. A is my brother's wife

Who made the stmt. and what r the realtions among

them


Answer(Not Sure)

• E is the mother in law of B.

B n C r brothers.A is the wife of C.D is the son

of C.

hence,statement 1 is told by B.

statement 2 is told by E.statement 3 is told by

D.statement 4 is told by B.


Answer (Not Sure)

• 1.B; 2. E; 3. D; 4. C • B and C are brothers. A is B's wife. D is

C's child. E is A's mother.


Q.9The product of 5 different temperatures is

12.If all of then r integers then find all the

temperatures


Answer

• -2 * -1 * 1* 2* 3 = 12


Q.10There are 9 cities numbered 1 to 9.From

how many cities the flight can start so as to reach

the city 8 either directly or indirectly such that

the path formed is divisible by 3.

eg. 1368-Flights goes through 1-3-6-8.


Answer

• Start from 1: 1368, Start from 2: 2358, Start

from 3: 378, Start from 4: 48, Start from 5:

528, Start from 6: 678, Start from 7: 78,

Why start from 8???, Start from 9: 918. So

flights can start from all 8 other cities.


Q.11Replace each letter by a digit. Each letter must be represented by

the same digit and no beginning letter of a word can be 0.

O N E

O N E

O N E

O N E

-------

T E N

-------


Answer

182

+ 182 O=1;N=8;E=2

+182

+182

=728


Q.12Ann, Boobie, Cathy and Dave are at their monthly

business meeting. Their occupations are author, biologist,

chemist and doctor, but not necessarily in that order. Dave

just told the biologist that Cathy was on her way with

doughnuts. Ann is sitting across from the doctor and next

to the chemist. The doctor was thinking that Boobie was a

goofy name for parent's to choose,but didn't say anything.

What is each person's occupation?


Answer (not sure)

• ANN- BIOLOGIST (confirmed) • BOOBIE- CHEMIST • CATHY- AUTHOR • DAVE- DOCTOR


Answer (not sure)

• CATHY=DOCTOR • DAVE=Chemist • ANN=Biologist... • BOOBIE=Author.... • They are sitting like this • Boobie.........Cathy • . . • . . • . . • Ann...............Dave


Q.13Sometime after 10:00 PM a murder took

place. A witness claimed that the clock must

have stopped at the time of the shooting. It was

later found that the postion of both the hands

were the same but their positions had

interchanged. Tell the time of the shooting

(both actual and claimed).


Answer

• Time of shooting = 11:54 PM

Claimed Time = 10:59 PM


lets say

murder takes place at h2 : m2 , meaning h2 hrs and m2 minutes...

also let the claimed time be , h1 : m1

we know that angle swept by hr hand in 1 hr=30 degree

and angle swept by min hand in 1 min=6 degree

now as per question , the hr hand at one time will sweep same angle

with respect to standard 12 o clock position

as the minute hand from the other time ....

so we can get two eqns as ,

6 m1 = 30 h2 + (m2 / 2) ........................................(a)

6 m2 = 30 h1 + (m1 / 2) ........................................(b)

now adding (a) & (b)

11(m1 + m2) = 60 (h1 + h2) .............................(c)

also, we get from (a) & (b) ,

13(m1 - m2) = 60(h2 - h1) .............................(d)

• now if we take , h1 & h2 as 10 & 11 repectively ,

from (c) we have m1 + m2 = 114.54 ................(e)

if we take , h1 & h2 as 11 & 12 repectively ,

from (c) we have m1 + m2 = 120

for that m1 = m2 =60 ....which would correspond to same time on clock

....hence not possible as per question ,

if we take , h1 & h2 as 11 & 12 repectively ,

from (c) we have m1 + m2 > 120 , which is not possible ...

and so on ...


• we cant take h1 and h2 less than 10 , as murder takes place after 10 pm... so putting the values of h1 and h2 in (d), we get m1 - m2 =4.6153 ........................(f) from (e) & (f) , m1= 59.577 m2=54.9623

hence the claimed time is 10 : 59.577

and the actual time of murder is 11 : 54.9623


14. Next number in the series is 1 , 2 , 4 , 13 , 31 , 112 , ?

Answer

Base 5 means

to use 1,2,3,4,5 only for finding numbers ,in this manner numbers will be

1,2,3,4,5,11,12,13,14,15,21,22,23,24,25,31,32,33,34,35,41,42,43,44,45,51,52,

53,54,55,111,112,113,114,115,121,122,123,124,125,.......

This series is written in base 5 numbers for decimal numbers

1,2,4,8,16,32,64 so next number is 224 .

224 in base 5 = 64 in base 10.


Q.15 Shahrukh speaks truth only in the morning

and lies in the afternoon, whereas Salman

speaks truth only in the afternoon. A says that B

is Shahrukh. Is it morning or afternoon and who

is A - Shahrukh or Salman?


Answer

• there are 4 cases • 1)it is morning and A is shahrukh, but is invalid because Shahrukh speaks truth

only in the morning

• 2)it is morning and A is salman,it may be the answer because Salman speaks

truth only in the afternoon and we don,t know what does he speak (truth or lie) in

morning

• 3)it is afternoon and A is shahrukh,it may be possible that he is telling a lie so

this may be the answer • 4)it is afternoon and A is salman,this must be the answer because Salman speaks

truth only in the afternoon. Compiled By: Prof. Ashwani Joshi

Practice Sets on CT


Q.16Two trains starting at same time, one from

Bangalore to Mysore and other in opposite

direction arrive at their destination 1 hr and 4

hours respectively after passing each other.

How nuch faster is one train from other?


Answer

• Let the time required to reach the meeting point is t, so the meeting

point would be at a distance of u*t and v*t from the two stations.

Now according to the given condition u*t = v*4 and v*t = u*1

on taking the ratio of these 2 equations, we have u/v = 4v/u or u/v

= 2/1


• let s1-peed of train from bangalore to

mysore(train1) s2- speed of train from mysore to

bangalore(train2) and x be the distance from B to M

and a be the distance from bangalore till meet point

(i.e.)train1 travels a km and train2 travels x-a km

time taken by train1 to travel a=time taken by train2 to travel x-

a a/s1=x-a/s2, s1/s2=a/x-a

time taken by train1 to travel x-

a=1hr x-a/s1=1, x-a=s1

time taken by train2 to travel

a=4hrs a/s2=4, a=4s2

therefore s1/s2=4s2/s1

s1^2=4s2^2

s1:s2=2:1

train1 speed=twice the speed of train2


Q.17 There are 6 volumes of books on a rack kept in

order ( ie vol.1, vol. 2 and so on ). Give the position

after the following changes were noticed. All books

have been changed Vol.5 was directly to the right of

Vol.2 Vol.4 has Vol.6 to its left and both weren't at

Vol.3's place.Vol.1 has Vol.3 on right and Vol.5 on

left. An even numbered volume is at Vol.5's place

Find the order in which the books are kept now.


Answer

• The Order in which the books are kept now

are:

Vol.2, Vol.5, Vol.1, Vol.3, Vol.6, Vol.4


Q.18 I Bought A Car With A Peculiar 5 Digit

Numbered License Plate Which On Reversing

Could Still Be Read. On Reversing Value Is

Increased By 78633.Whats The Original Number

If All Digits Were Different?


Answer

Only 0 1 6 8 And 9 Can Be Read Upside Down.

So On Rearranging These Digits, We Get The

Answer As

10968.

Answer(Alternate way)

• Only 0, 1, 6, 8, and 9 can be read upside down.

So on rearranging these digits we get the answer as 10968.

answer is 10968.

89601

10968

------

78633

------

i)we can't read 2,3,4,5,7 while they are reversed.

ii)so that number is built with 1,6,8,9,0.

iii) difference between both numbers is 78633.

iv)both the numbers are 5 digits. units place difference is 3, so 0(zero is not at the both the ends)

v) 10 thousands place difference is 7. units place difference is 3

this is possible only through 8,1 numbers( because 8-1= 7 and 11 -8 =3)(another pair to getting difference 3 is (9-6) but 6-9 not equal to 7 so this is not

the pair),

So in actual number plate ones place is 8 and ten thousands place is 1.

vi) in thousands place we have to get the difference is 8 and tenths place difference have to get 3 ( the only one possible way is ((9-1) -0)and (10-1-6)

because( 1, 8 already placed at the end positions) .

Considering all above cases

actual number is 10968



Q.19Salay walked 10 m towards West from his

house. Then he walked 5 m turning to his left.

After this he walked 10 m turning to his left and in

the end he walked 10 m turning to his left. In what

direction is he now from his starting point?

(A) South (B) North (C) East (D) West (E) None of

these


Answer: North


Q.20Manish goes 7 km towards South-East from his

house, then he goes 14 km turning to West. After

this he goes 7 km towards North West and in the end

he goes 9 km towards East. How far is he from his

house?

(A) 5 km (B) 7 km (C) 2 km (D) 14 km (E) None of

these


Answer

Practice Sets of ICD By: Prof. Ashwani Joshi Department of Electrical Engineering

• x^2 + x^2 = 7^2 [Pythagoras theorem ] • => x = 7/√2 • y = 14 -2x = 14-7√2 • Total distance covered from starting poit to

final point = 9-(14-7√2) • => 7√2 - 5.


Q.21There are two balls touching each other

circumferentially. The radius of the big ball is 4 times the

diameter of the small all. The outer small ball rotates in

anticlockwise direction circumferentially over the bigger

one at the rate of 16 rev/sec. The bigger wheel also rotates

anticlockwise at N rev/sec. What is 'N' for the horizontal

line from the centre of small wheel always is horizontal.


Answer


Q.22There is a safe with a 5 digit No. The 4th

digit is 4 greater than second digit, while 3rd

digit is 3 less than 2nd digit. The 1st digit is

thrice the last digit. There are 3 pairs whose sum

is 11. Find the number.


Answer

Let the five digit number be :abcde

• d=b+4.....(i) • c=b-3.....(ii) • a=3e......(iii) • As given pair of three =11 so let pair of dc is 11. • Add equation 1 and 2 and equate to 11 • i.e 2b-1=11; then b=5 • Now acording to question if b=5 then d=9;c=2 • As given pair of three =11 i.e 6+5=11,cd=2+9=11 and e=2; de=9+2=11 • So the no is 65292

Practice Sets of ICD By: Prof. Ashwani Joshi Department of Electrical Engineering

Q.23 13kigs and 6 libs can produce 510 tors in

10 hrs, 8 kigs and 14 libs can produce 484 tors in

12 hrs.Find the rate of production of tors for kigs

and libs. Express the answer in tors/hr.


Answer(Not Sure)

• let, Kigs---> x & Libs---> y

13x+6y = 510/10

8x+14y = 484/12

So, x=236/67 & y=349/402

x+y=1765/402=4.39 (approx.)

Ans =4.4 tors/hr.


Q.24 In 4 years, Raj’s father age twice as Raj.

Two years ago, Raj’s mother’s age is twice as

Raj. If Raj is 32 years old in eight years from

now, what is the age of Raj’s mother and father?


Answer

• father-52, mother- 46


Q.25 persons say these statements.

A says either Democratic or liberal wins

the elections.

B says Democratic wins.

C says neither democratic nor liberal wins the

election.

Of these only one is wrong. who wins the election?


Answer

• c is false....so democratic will win


26) Ramesh sit around a round table with some other men.

He has one rupee more than his right person and this

person in turn has 1 rupee more than the person to his

right and so on, Ramesh decided to give 1 rupee to his

right & he in turn 2 rupees to his right and 3 rupees to his

right & so on. This process went on till a person has 'no

money' to give to his right. At this time he has 4 times the

money to his right person. How many men are there along

with Ramesh and what is the money with poorest fellow.



Answer

• Here, consider there are n number of persons sitting on the table.

Let Ramesh has Rs. x.

Then the person to his right will have (x-1) then to his right will have (x-2)

and so on till the person to the left of ramesh have Rs (x-(n-1)) •

Here it is said that x gives Re 1 to his right and he in turns give Rs2 to

his right and the process continuess untill we get a person who cannot give to

his right i.e he is let with no money. •

In the 1st round person to the right will be left with Rs x-2, to his right

will have x-3 and so on and the person to the left of Ramesh have Rs (x-n)

And now Ramesh has Rs(x +n-1). •

In the 2nd round person to the right will be left with Rs x-3, to his

right will have x-4

and so on and the person to the left of Ramesh have Rs (x-(n+1))

And now ramesh has Rs(x + 2(n-1)) •


• Let this process continues for r

rounds Then

person to the right of Ramesh has (x-r-1)

person to the left of Ramesh has (x-(n+r-1))

and Ramesh has (x + r(n-1)) •

Now we have a condition that we stop when we have a person who has 0 sum

Here person to the left of Ramesh has Rs.0

i.e x=n+r-1

•

Also ramesh has 4 times the sum of the person to his right

i.e x+r(n-1) = 4(x-r-1)

i.e 3x -4 = 3r + nr

=> 3(n+r-1) - 4 = 3r + nr

=> 3n = nr +7 •


• Now if the process completes in 1 round then r=1

we get 2n = 7

this can not be the number of persons •

Now when r=2

we get n=7

=> x = 8 •

Thus Ramesh has Rs. 8 and the person to his right will have 7,6,5,4,3,2 •

Proof:

In the 1st Round

Ramesh's right = 6

Ramesh's left = 1

Ramesh = 14 •

In the 2nd round

Ramesh's right = 5

Ramesh's left = 0

Ramesh = 20 •

and 20 = 4(5)


27) The number of multiples of 10 which are

less than 1000, which can be written as a sum of

four consecutive integers is

a. 50 b. 100 c. 150 d. 216


Answer

• Total no. of multiples of 10 = 1000/10 =

100 now,

10=1+2+3+4

But 20 can not be written as the sum of 4 consecutive no.s

since some of the multiples of 10 can not be written as the sum of 4 consecutive

no.s, the answer should be less than total no. of multiples of 10 (i.e. less than 100).

In the options only A. is less than 100.

therefore ans. is option A.


28) Venkat has 1boy & 2daughters.The product

of these children age is 72.The sum of their ages

give the door number of Venkat. Boy is elder of

three. Can you tell the ages of all the three?


Answer(Not sure)

• 2 , 6 & 6


• 29) L:says all of my other 4 friends have

money M:says that P said that exact one has

money N:says that L said that precisely two

have money O:says that M said that 3 of others

have money. P:Land N said that they have

money. All are liers. Who has money & who

doesn't have?


Answer

• Since L,N,P said that they have money and since they are (perfect) liars, it turns out that L has no money, N has no Money and P has no money. Let us assume that M and O have money and verify the statements. L says that M,N,O,P all have money. This has already been shown to be a lie. P says L and N have money and we know that is a lie also

M said that P says that exactly one person has the money. We know that is a lie as well (Both ways: M did not say one person has the money and nor does one person out of L & N have money) N said that L said that exactly two have the money. Again this is a lie, as M named four, and out of those four, only one really has money So, the right answer would be: L, N and P have no money . O has money. We cannot determine if M has money or not, with the statements given


30. A person has to go both Northwards &

Southwards in search of a job. He decides to go by

the first train he encounters. There are trains for

every 15 min both southwards and northwards. First

train towards south is at 6:00 A.M. and that towards

North is at 6:10. If the person arrives at any random

time, what is the probability that he gets into a train

towards North.


Answer

• Let's simulate a 60 minute time period: Period of 60 Minutes broken into intervals of 5 minutes each: 0 - 5 - 10 - 15 - 20 - 25 - 30 - 35 - 40 - 45 - 50 - 55 - 60(or "0" again)

Arrival of train : ( S = south train, N = north train, X = no train arrives at that particular time) S - X - N - S - X - N - S - X - N - S - X - N - S TO MAKE IT EASY TO UNDERSTAND I HAVE WRITTEN THE SAME THING AGAIN. 0 - 5 - 10 - 15 - 20 - 25 - 30 - 35 - 40 - 45 - 50 - 55 - 60 S - X - N - S - X - N - S - X - N - S - X - N - S 0 10 5 10 5 10 5 10 5 The line written immediately above (that is the 3rd line of data) has numbers corresponding to "N" and "S" which shows how many minutes had a person to wait till he gets the "First Train". Therefore,

N = 10 + 10 + 10 + 10 = 40 Minutes S = 0 + 5 + 5 + 5 + 5 = 20 Minutes Therefore in 40 minutes of standing time for the train he will get N train and in 20 minutes of standing time for the train he will get S train. You will also see that this is the schedule for every hour after 6.00 A.M.

This means that the probability that he will get N train is = 40 Minutes / 60 Minutes = 2/3 = 0.67 = 67.67% Also the probability that he will get S train is = 20 Minutes / 60 Minutes = 1/3 = 0.33 = 33.33%


31) A person has his own coach & whenever he goes to railway station

he takes his coach. One day he was supposed to reach the railway

station at 5 O'clock. But he finished his work early and reached at 3

O'clock. Then he rung up his residence and asked to send the coach

immediately. He came to know that the coach has left just now to the

railway station. He thought that the coach has left just now to the

railway station. He thought that he should not waste his time and

started moving towards his residence at the speed of 3 miles/hr. On

the way, he gets the coach and reaches home at 6 o'clock. How far is

his residence from railway station?


Answer

• He walked for 1.5 hrs and coach travelled in one side for 1.5

hrs instead of 2 hrs to save 0.5 hrs one side journey of coach. • So Coach speed is 3 times speed of man i.e. 9 mph. • Total distance of stn from Home = 1.5( 3+9) = 1.5*12= 18 miles


32) Radha,Geeta & Revathi went for a picnic. After

a few days they forgot the date, day and month on

which they went to picnic. Radha said that it was on

Thursday, May 8 and Geeta said that it was

Thursday May 10. Revathi said Friday Jun 8. Now

one of them told all things wrongly, others one thing

wrong and the last two things wrongly. If April 1st

is Tuesday, what is the right day, date and month?


Answer

• Thursday, May 8


33). There is 66x33m rectangular area. Ram is 11/8 times

faster than Krishna. Both of them started walking at

opposite ends and they met at some point then, Ram said

"See you in the other end" Then they continued walking.

After some time Ram thought he will have tea so he

turned back walked back 15 meters then he changed his

mind again and continued walking. How much Krishna

has traveled by the time they meet?


Answer

• let x be the distance between the point they first

met • total time taken by the two willbe equal • so (x+30)*8/11 = (198-x) • x= 102m • distance travelled by krishna= 198-102 = 96m


Q.34X Z Y+X Y Z = Y Z X Find the three digits

Note: No digit are zero(xyz not zero)

Answer: X=4,Y=9,Z=5....459+495=954


Q.35. All members belonging to D are

members of A. All members belonging to E are

members of D. All members belonging to C are

members of both A & D. Some members of A

does not belong to D. All members belonging

to D are members of E. who not belonging to

one another?


Answer


Q.36. There are twelve consecutive flags at an

equal interval of distance. A man passes the 8th

flag in 8 seconds. How many more seconds will

he take to pass the remaining 4 flags?


Answer

• let the 1st flag i placed at the origin and the

remaining on the X-axis.......then the cordinate

og 8th flag is (7,0)..therefore distance travelled

is 7 units in 4 second ......and cordinate of 12th

flag is (11,0)..there r 4 units ....so tym taken is

(8*4)/7=4.57 secnds



Alternate Way

• he start at the first flag and then he crosses the

remaining 7 flags at 8secs.therefore his speed is

8/7=1.14sec.so if his speed is constant then he

will cross

the remaining 4 flags at

4*1.14 = 4.56secs


Q.37. A person has to cover the fixed distance

through his horses. There are five horses in the cart.

They ran at the full potential for the 24 hours

continuously at constant speed and then two of the

horses ran away to some other direction. So he

reached the destination 48 hours behind the

schedule. If the five horses would have run 50 miles

more, then the person would have been only 24

hours late. Find the distance of the destination.


Answer

• Suppose his actual speed is 'v' with 5 horses, If he travelled that 50 miles with 5 horses the time taken wud b 50/v, which equals time taken with 3/5th speed minus 24hrs 50/v = 50/(3v/5) - 24; so, v = 25/18; Now, suppose after 1st 24 hrs he takes 't' hrs toreach his destination, then vt = (3v/5)(t + 48); vt = (3v/5)(t+48) t = 72

total time = 72+24 = 96 distance = 400/3


Q.38A boat M leaves shore A and at the same

time boat B leaves shore B. They move across

the river. They met at 500 yards away from A

and after that they met 300 yards away from

shore B without halting at shores. Find the

distance between the shore A & B.


Answer

• The boats first met after 500yards from A. • Let the total distance between A and B be x. • then, 500/a = x-500/b, • where, a = speed of A, b =speed of B. • Assuming both boats are coming back to their original start

place without halting at the shores, • Distance coverred by A = x + 300 • Distance covered by B = 2x - 300 • x+300/a = 2x-300/b • From above, • 500/x-500 = x+300/2x-300 • Solve, for x = 1200


Q.39The Master says to his grandmaster that I

and my three cousins have ages in prime nos.

only. Summation of our ages is 50.

Grandmaster who knows the age of the master

instantly tells the ages of the three cousins. Tell

the ages of three cousins.


Answer

• 43,3,2,2 or 3,5,11,31, - sum of ages of all 4 cousin is

50 • 2+2+3+43=50 • ages can be 2,2,3,43 yrs

• OR

• 5+3+11+31=50 • ages can be 3,5,11,31 yrs


Q.40 Food grains are to be sent to city from

godown. Owner wants to reach the food grains at 11

O' Clock in the city. If a truck travels at a speed of

30km/hr then he will reach the city one hour earlier.

If the truck travels at a speed of 20km/h then he will

reach the city one hour late. Find the distance

between the godown to city. Also with which speed

the truck should travel in order to reach at exactly

11 'O clock.


Answer

• Let distance be x km and original time be t hr, when he

travels at constant speed, say s kmph.

Clearly, x = st.

Now, x=30(t-1) and x=20(t+1). Solving these to

simultaneous linear eqns, we get x=120 km and t=5 hr. So,

distance between city and go-down=120km. To reach

exactly at 11 o'clock, he must travel at speed s=x/t = 120/5

= 24 kmph


Q.41. There are five persons A,B,C,D,E whose

birthdays occur at the consecutive days. Birthday

of A is some days or day before C & birthday of

B is exactly the same days or day after E. D is

two days older than E. If birth day of C is on

Wednesday then find out the birthdays of other.


Answer

• Their birthday sequence is

DAECB.

If birth day of C is on Wednesday

then Birthday of A.... Monday

For B..... Thursday

D....... Sunday

E...... Tuesday


Q.42 A fly is there 1 feet below the ceiling right

across a wall length is 30m at equal distance

from both the ends. There is a spider 1 feet above

floor right across the long wall eqidistant from

both the ends. If the width of the room is 12m

and 12m, what distance is to be travelled by the

spider to catch the fly, if it takes the shortest

path.Practice Sets on CT Compiled By: Prof. Ashwani Joshi


Answer

• its 24 simply.

what fly is expected to do is - Go down 1' on the

floor, then cross the floor and then go up.

So its 1 + 12 + 11 = 24 m


Q.43Six persons A,B,C,D,E &F went to soldier

cinema. There are six consecutive seats. A sits in

the first seat followed by B, followed by C and

so on. If A taken on of the six seats, then B

should sit adjacent to A. C should sit adjacent to

A or B. D should sit adjacent to A, B or C and so

on. How many possibilities are there ?


Answer

• First we have to arrange A, there is 1 method

for it, for second person B, there are 2 methods

one left and one right, for third 2 methods are

there same as for B similarly for others, so

total number of methods = 1*2*2*2*2*2 = 32


Q.44Suppose there are four grades A, B, C, D. (A is the best

and D is the worst) 4 persons Jack, Jean, Poul and Lucy wrote

the final exam and made the statements like this:- 1. Jack: If I

will get A then Lucy will get D. 2. Lucy: If I will get C then

Jack will get D. Jack grade is better than Poul grade. 3. Jean: If

Jean doesn't get A then Jack will not get A. 4. Poul: If Jack get

A, then Jean will not get B, Lucy will get C, I won't either A or

B. If all the above statements are true, then which person will

get which grade?


Answer

• If jack gets C which is a better grade than Poul whose

rank is D.than Lucy will get B and Jean will get A.

Jean->A

Lucy->B

Jack->C

Poul->D


Q.45 Every man dances with 3 women and every

woman dances with 3 men.And also 2 men have

2 women in common in the party. How many

people attended the party?


Answer

• Men -- M1, M2... etc

Women -- W1, W2.. etc

the pair can we arranged this way -- M1-

W1; M1-W2; M1W3 -- FIRST PAIR

Now, we have a condition -- each men has exactly 2 women

in common.

so, we need 1 extra woman for next pair

M2-W1; M2-W2; M2W4


• LIKEWISE, WE CAN ARRANGE MEN FOR W4 AS WELL. M3-W1; M3-W3; M3W4 Last Pair; -- M4-W2; M4-W3; M4-W4 TOTAL -- 4 Men -- M1 M2 M3 M4 4 Women -- W1 W2 W3 W4 = 8

Q.46. A survey was taken among 100 people to find

their preference of watching t.v. programs. There

are 3 channels. Given no of people who watch at

least channel 1, at least channel 2,at least channel 3,

no channels at all, at least channels 1 and 3, at least

channels 1 and 2, at least channels 2 and 3. Find the

no of people who watched all three.


Answer

• Consider the standard Venn diagram consisting of three circles

mutually intersecting, each circle representing the set of people

watching each channel. Let these be A (channel 1), B (channel 2) and C

(channel 3). Name the portions in the figure as follows:

The portion in A alone: a

The portion in B alone: b

The portion in C alone: c

The portion common to B and C only: d

The portion common to C and A only: e

The portion common to A and B only: f

The portion common to A, B and C: g


• Now, these circles are all enclosed in a rectangle representing the entire

population. The portion inside the rectangle, but outside all the circles

be called r.

Given:

1. at least channel 1 : a+f+g+e

2. at least channel 2 : b+f+g+d

3. at least channel 3 : c+e+g+d

4. no channels at all : r

5. at least channels 1 and 3 : e+g

6. at least channels 1 and 2 : f+g

7. at least channels 2 and 3 : d+g


• To find: no of people who watched all three:

g Given, a+b+c+d+e+f+g+r = 100

So, a+b+c+d+e+f+g = 100-r

This can be calculated, since r is given.

Substituting (5.) in (1.), (6.) in (2.) and (7.) in (3.),

we can calculate a+f, b+d and c+e.

Adding all these, we get a+b+c+d+e+f

Now, g = 100 - r - (a+b+c+d+e+f)

Q.47. There is an escalator and 2 persons move

down it. A takes 50 steps and B takes 75 steps

while the escalator is moving down. Given that

the time taken by A to take 1 step is equal to time

taken by B to take 3 steps. Find the no. of steps

in the escalator while it is stationary.


Answer

• If S is no of steps In The Escalator While It Is

Stationary. A Takes 50 Steps And B Takes 75 Steps

While The Escalator Is Moving Down.

Given That The Time Taken By A To Take 1 Step Is Equal To Time

Taken By B To

Take 3 Steps.

If A takes time 't' secs to take 50 steps, B takes (t/50)*(75/3) = t/2

secs Then speed of escalator remains same in 2 cases.

so (S-50)/t = (S-75)/2t

so S -50= 2s-150

s=100


Alternate

• If A takes 1 step in one second, then B takes 3 steps in one

second. If A takes t1 seconds to take 50 steps, then B takes

150 steps in t1 seconds.

For B, to take 150 steps he requires t1 seconds,

then to take 75 steps he requires t1/2 seconds.

So now, s1=50, t1 = t1 & s2=75, t2=t1/2

ans= (s1*t2 ~ s2*t1) / (t1 ~ t2) which gives 100.

so 100 steps is the answer


48. There are N coins on a table. There are two players A&B. You can

take 1or 2 coins at a time. The person who takes the last coin is the loser.

A always starts first.

1. If N=7, then a) A can always win by taking two coins in his first chance. b)

B can win only if A takes two coins in his first chance. c) B can always win

by proper play. d) none of the above. 2. A can win by proper play if N is equal to

a) 13 b) 37 c) 22 d) 34 e) 48 3. B can win by proper play if N is equal to

a) 25 b)26 c) 32 d) 41 e) none

4. if N<4, can A win by proper play always?


Answer

• 1. c because whether A takes 1 or 0, B has to

make sum of A+ his ,so that 1 is always left for

A. 2.e A can win by proper play when N is a

multiple of 3

3. e) b can always win by proper play by making

sum of takes of A and himself=3.

4.For n=2,it doesn't hold.


49. There are 4 parties A,B,C,D. There are 3

people x,y,z. X-says A or D will win. Y-says A

will not win. Z-says B or D will not win. Only

one of them is true. Which party won?


Answer

• If A wins, both X and Z are true.

If C wins, both Y and Z are true.

If D wins, both X and Y are true.

So, party B won. (Only Y is true)


50. 5 persons R,S,T,U,V are contesting for a medal.

Evaluation is over English, Maths, Physics,

Chemistry and Hindi. Toper will get 5 marks, least

will get 1 mark. No ties anywhere. R got 24 and

won the overall medal. V got first in Chemistry and

third in Hindi, T got consistent scores in 4 subjects.

Their final standings are in the alphabetical order.

What was the score of S in Chemistry?


Answer


51. There are five persons A,B,C,D,E whose

birthdays occur at the consecutive days. Birthday

of A is some days or day before C & birthday of

B is exactly the same days or day after E. D is

two days older than E. If birth day of C is on

Wednesday then find out the birthdays of other.


Answer

• Their birthday sequence is

DAECB.

If birth day of C is on Wednesday

then Birthday of A.... Monday

For B..... Thursday

D....... Sunday

E...... Tuesday


52. When Arthur is as old as his father Hailey is

now, he shall be 5 times as old as his son Clarke

is now. By then, Clarke will be 8 times older

than Arthur is now. The combined ages of Hailey

and Arthur are 100 years. How old is Clarke?


Answer

• Let assume clerk age as = X

then Arthur age will be = 5x

also Haily age will be same =5x

Now Clerk age becomes 8(5x)=40x

Sum of ther ages = 5x+5x=100

therfore x=10

That is clerk age is 10


53. If 5/2 artists make 5/2 paintings using 5/2

canvases in 5/2 days then how many artists are

required to make 25 paintings using 25 canvases

in 25 days?


Answer

• 5/2=25/X

x=50/5;

x=10;

5/2=25/10;

That is 5/2 artists r required to make 25 paintings.


Alternate

• here A=artists and P= painting C = canvases d=day

A is direct proportional Pand C but inverse proportional to

d so we can write

A==K*P*C/d here k is constant

solve

5/2=(K*5/2*5/2)/5/2

so k=1

A=P*C/d

A=25*25/25

A =25 day


54. There are 5 burglars and once went to a

bakery to rob it obviously. The first guy ate

1/2 of the total bread and 1/2 of the bread. The

second guy ate 1/2 of the remaining and 1/2 of

the bread. The third guy, fourth guy and fifth guy

did the same. After fifth guy there is no bread

left out. How many bread are there?


• First we create a general rule for amount of bread left when each burglar leaves

Lets assume we have x no of bread

At every step x/2 + 1/2 bread is eaten by the burglar

Therefore after each step compared to previous step we have [x-(x/2 + 1/2)] = x/2 -

1/2 bread left.

Now let us go to the problem

Now after 5th burglar leaves we have 0 bread left

Hence number of bread after 4th burglar leaves (or before 5th burglar enters)

is calculated by

x/2 - 1/2 = 0

Therefore x = 1


• Similarly after 4th burglar leaves we have 1 bread left Hence number of bread after 3th burglar leaves (or before 4th burglar enters) is calculated by x/2 - 1/2 = 1 Therefore x = 3

• Similarly after 3rd burglar leaves we have 3 bread left Hence number of bread after 2nd burglar leaves (or before 3rd burglar enters) is calculated by x/2 - 1/2 = 3 Therefore x = 7

• Similarly after 2nd burglar leaves we have 7 bread left

Hence number of bread after 1st burglar leaves (or before 2nd

burglar enters) is calculated by

x/2 - 1/2 = 7

Therefore x = 15

Similarly after 1st burglar leaves we have 15 bread left

Hence number of bread before 1st burglar enters is calculated

by x/2 - 1/2 = 15

Therefore x = 31····························· Ans


Answer

• (1/2 + 1/2) = 1

2(1 + 1/2) = 3

2(3 + 1/2) = 7

2(7 + 1/2) = 15

2(15 + 1/2) = 31


Q.55Two boats start from opposite banks of river

perpendicular to the shore. One is faster then the

other. They meet at 720 yards from one of the ends.

After reaching opposite ends they rest for 10mins

each. After that they start back. This time on the

return journey they meet at 400yards from the other

end of the river. Calculate the width of the river.


Answer

• Let us assume that width of river d yards and

speed of boats - x and y yards/min respectively.

Hence the two equations are :1) (d-720)/x =

720/y2) (d/y+10+400/y) = (d/x + 10 + (d-

400)/x)Solving the two equations We get

d=1760 yard


Q.56Basketball Tournament organizers decided

that two consecutive defeats will knock out the

team. There are 51 teams participating. What is

the maximum no. of matches that can be played.


Answer

• Assuming there is no particular order and teams left standing play each other again until 2 defeats. T1 can win 50 games in a row (don't play themselves). T2 - T51 have 1 defeat. T2 can then win 49 games in a row (don't play themselves and have lost to T1). Every other team except T1 and T2 now have 2 defeats. -> T1=0 and T2=1 Team1 loses to T2 -> T1=1 and T2=1 Then either T1 or T2 loses. Total = 50 + 49 + 1 + 1 = 101


Q.57 A person was going through train from

Bombay to Pune. After every five minutes he

finds a train coming from opposite direction.

Velocity of trains are equal of either direction. If

the person reached Pune in one hour then how

many trains he saw in the journey ?


Answer


Q.58There are two families Alens and smiths. They have two children

each. There names are A,B,C,D whose ages are different and ages are

less then or equal to 11. The following conditions are given:-

i) A's age is three years less then his brother's age . ii) B is eldest among the four. iii) C is half the age of the eldest in Alens family. iv) The difference in sum of the ages of Alens children and

smiths children is same as that of five years ago. Find the ages of all the children.


Answer

• B- 10, D-9, A-6, C-5

soln- (B+C)- (A+D)=0

[(B-5)+(C-5)]-[(D-5)+(A-5)]=0


Answer

• AS IT IS CLEARLY GIVEN IN THE QUESTION THAT HE REACHES

PUNE IN ONE HOUR, AND SEES ONE TRAIN AFTER EVERY FIVE

MINUTES.... SO THIS HAS NOTHING TO DO WITH VELOCITY OF

APPROACHING TRAIN...SO HE'LL SEE 12 TRAINS ON HIS WAY....

Or • 13...at the start of his journey (0 hr), 1 train passes. after that next train at

5, 10, 15...60 (total 12)... 12+1=13...


Q.59There are six cards in which it has two king

cards. all cards are turned down and two cards

are opened

a) what is the possibility to get at least one king. b) what is the possibility to get two kings.


a)

POSSIBILITY TO GET AT LEAST ONE KING

IS : 2C1*4C1/6C2 + 2C2/6C2 = 8/15+1/15=3/5

b)

P0SSIBLITY TO GET TWO KINGS

IS 2C2/6C2=1/15


Alternate Solution

a)1. You can pick up either of the king, so => you can pick a king and

other card by 5 different ways, but since you have 2 kings(they are

different cards) you have 9 different ways to choose a king and

another card.

2. All ways you can pick 2 card are:

• with the first card you have 5 choices ;

• with the second, 4 choices;

• and so on...=>5+4+3+2+1=15

Answer: 9/15=3/5=60%


b) This is easier, you have only one way to get

the two kings so 1;

and the answer is : 1/15.


Q.60There are 5 persons a,b,c,d,e and each is wearing a black

or white cap on his head. a person can see the caps of the

remaining 4 but can't see his own cap. a person wearing white

says true and who wears black says false.

i) a says i see 3 whites and 1 black ii) b says i see 4 blacks iii) e says i see 4 whites

iiii) c says i see 3 blacks and 1 white.


Answer

• Let A – Black B – White C – White D – Black

• E - Black

This cannot be true bcoz if B is white, then he says true n if he

say true than c cannot be white bcoz he sees 4 black

So possible answer is

A Black B Black C White D White

E Black



Q.61 There are two women, kavitha and shamili and two

males shyam, aravind who are musicians. Out of these

four one is a pianist, one flutist, violinist and drummer.

i) Across aravind knocks pianist. ii) Across shyam is not a flutist. iii) Kavitha's left is a pianist. iv) Shamili's left is not a drummer. v) Flutist and drummer are married.


• Violin = Shyam

Flutist = Aravind

Drummer = Kavita

Pianist = Shamili

Shyam(Violin) Aravind(flute)

Shamili(piano) Kavita(drum)


• The above seating arrangement satisfies the given conditons. across aravind is pianist as shamili across shyam is drummer not flutist kavitas left is pianist as shamili shamili left is shyam who is not drummer

aravind and kavita are married.

Q:62Persons A and B. Person A picks a random no. from 1 to

1000.Then person B picks a random no. from 1 to 1000. What

is the probability of B getting no. greater then what A has

picked.


Answer

• Probability of B getting greater no than A=

P(B)/ ( p(A)+p(B)) • P(A)=1/1000 P(B)=1/1000

Therefore ans = (1/1000) / (2/1000) = 1/2


Q.63The seven digits in this subtraction problem are 0, 1, 2, 3,

4, 5 and 6. Each letter represents the same digit whenever it

occurs.

D A D C B

- E B E G

----------

B F E G

----------


Answer


Q.64 The Jones have named their four boys after

favorite relatives; their friends, the Smiths, have done

the same thing with their three boys. One of the families

has twin boys. From the following clues, can you

determine the families of all seven children and their

ages?


i) Valentine is 4 years older than his twin brothers. ii) Winston, who is 8, and Benedict are not brothers.

They are each named after a grandfather. iii) Briscoe is two years younger than his brother

Hamilton, But three years older than Dewey. iv) Decatur is 10 years old. v) Benedict is 3 years younger than Valentine; they are

not related. vi) The twins are named for uncles.


Explanation:

From the given clues it is clear that benedict is not in the same group as

winston and valentine (clue 2 and 5) which means winston and valentine are

in the same group,also the twin brothers will be in the group of valentine and

winston(clue 1)briscoe and hamilton get eliminated from the group of valntine

& winston coz they are brothers (clue 3)so they belong to the group of

benedict.Left ones are Dewey and Decatur. Since group of valentine contains

twin brothers so Dewey goes to their group and Decatur to other group. Ages

can be determined using the clue for ages given. Also given in ques that Jones

have 4 sons and smiths have 3.


Answer

• Smiths- Valentine(12),Winston(8),Dewey(8) [winston and dewey are twins] • Jones-Benedict(9),Brisoe(11),Hamilton(13),Decatur(10)


Q.65 Motorboat A leaves shore P as B leaves Q;

they move across the lake at a constant speed.

They meet first time 600 yards from P. Each

returns from the opposite shore without halting,

and they meet 200 yards from Q. How long is

the lake?


• p----------- x----------- q

• a-- > <-- b

• <-- 600--><--- (x-600)--- >

• <--- (x-200)--- ><--200-- >

• let speed of a and b are a and b kmph resp. and distance b/w pq is x. • If a covers the distance of 600 in 't' hours and b covers x-600 at same time.

• so 600/a=(x-600)/b ------eq.1

• Again they meet when a is 200 from q that means a covers the distance of (x-

600)+200 and at same b covers (600)+(x-200)

• so {(x-600)+200}/a={(600)+(x-200)}/b --------eq.2

• solve 1 and 2 u'll get x=1600,0 obviously 1600 is the answer


Documents

Important Questions & Answers for Day-1 Campus Drive by · • 1. sum of ages are same. 2. also, its been said dat jim is dorthy's brother so jim kan be wid virginia or jane. 3. but