Puzzles

Wednesday, June 30, 2004

62 -

62. Mr. Sekhar and Ms. Sekhar are having conversation like this:
Mr. Sekhar said to Ms. Sekhar: "Give me three quarters of what you
have , i will add it with what i have, totally to buy a house at
indiranagar for 5000/-,remaining at hand with you can be bought the
running stream and groove".
Ms.Sekhar, said ,"No, No, give me two thirds of what you have , i will
add it with what i have ,totally we can buy the house ,and the groove and
running stream we can buy with the remaining money we have".
can you find the money required to buy the groove and stream?

Let X be the Money with Mr.Sekhar and Y be the money with Ms.Shekar.

X + (3/4)Y = 5000
(2/3)X + Y = 5000

Solving we get X = 2500 and Y = 10000/3.
so value of the stream and groove is Y/4 = X/3 = 2500/3

63. A man passed 1/6th of his life in childhood ,1/12th as youth,
1/7th more as a bachelor; five years after his marriage a son was born who died
four years before his father at half his final age. What is the total age of the man?

Let X be the total age

X/6 + X/12 + X/7 + 5 + 4 = X/2

solving we get X = 84

64. A thief broke into a jewellery shop & thought of taking all the diamonds with him but while he was leaving, came to his better sense & thought of taking half with him. But he could not resist & took two more extra and left. A second thief came and took half of the remaining & two more. Then a third thief came and took half of the remaining and two more. Then a fourth thief came and did the same. The fifth thief came & found no more diamond for him. What was the initial no. of diamonds?

working backwards.
0
4
12
28
60

65. A confused bank teller transposed the dollars and cents when he cashed a check for Ms Smith, giving her dollars instead of cents and cents instead of dollars. After buying a newspaper for 50 cents, Ms Smith noticed that she had left exactly three times as much as the original check. What was the amount of the check?

Let X be the dollars and Y be the cents

3(100X + Y) = 100Y + X - 50
300X + 3Y = 100Y + X - 50
97Y - 299X = 50

solving for X and Y we have the values 18 and 56.

Tuesday, June 29, 2004

52 - 61

52. A cyclist got his tyre punctured when he had covered two third of
the distance to be covered.Finishing on foot,He takes twice the time
taken before to reach the destination.How fast does he ride than
walking?

Let T be the usual time taken.
Let D be the distance.
Let S1 and S2 be the speed of cycling and walking.
So extra time taken for covering 1/3 of the distance is another T.

D/S1 = T; S1 = D/T
(2/3)D/S1 + (1/3)D/S2 = 2T; -- 1

solving 1 using S1 = D/T we have S2 = D/4T;
So S1:S2 is 4:1 he rides 4 times faster than walking

53. A person travels in a car with uniform speed. He observes the milestone,
which has 2 digits. After one hour he observes another milestone with same
digits reversed. After another hour he observes another milestone with
same 2 digits also containing a 0. Find the speed of the car?

2 Digit no and the last no is a 3 digit no.
So one of the digits is 1 as the car speed is not more than 100 Kms.
The gap between the no and the reversed no should be same as the reversed no and
3 digit no.

15 16 17 18 19
51 61 71 81 91
105 106 107 108 109

only 16, 61, 106 match the above rule. so the speed of the car is 45 Kmph

54. One quarter of the time till now from midnight and half of the time
remaining from now up to midnight adds to the present time. What is the
present time?

Let the current time be X minutes from Midnight.

X/4 + (24*60-X)/2 = X
solving we get X = 48 * 60 / 5 Minutes giving the time is 9:36 AM

55. Three persons A, B &C went for a robbery in different directions and they
stole one horse, one mule and one camel. They were caught by the police
and when interrogated gave the following statements

A: B has stolen the horse
B: I didn’t rob anything.
C: both A & B are false and B has stolen the mule.

The person who has stolen the horse always tell the truth and
The person who has stolen the camel always tell the lie.

Find who has stolen which animal?

B lies so A also lies.
so C is correct B has stolen the Mule.
C has stolen the horse and A has stolen the Camel.

56. A, B, C, D & E are having their birthdays on consecutive days of the week
not necessarily in the same order. A ‘s birthday comes before G’s as many
days as B’s birthday comes after E’s. D is older than E by 2 days. This
time G’s birthday came on Wednesday. Then find the day of each of their
birthdays?

Since there are only 5 people and D and E are 2 days apart
the Gap between A and G and E and B has to be 2 days.

so The order of the birthdays
DAEGB and given G is born on Wednesday we have
D = Sunday
A = Monday
E = Tuesday
G = Wednesday
B = Thursday.

57. a tin sheet of 34 x 34 inch. It has to be put on a square of the same size.
the carpenter puts the nails in such a way that there r 35 nails on each side of the square.
find the total no of nails?

Leaving out the common nails we have 33 nails per side so
33 * 4 + 4 in the corners = 136 nails

58. A and B starts palying a chess tournament with one match everyday.
The one who looses gives a chocolate to the other. at the end of the
tournament B gives 8 chocolates to A. But A says that "i have won more matches than
B and B has won 20 matches".Find the total no of matches.

A should have won 20 + 8 = 28 matches. B won 20 matches. So total is 48 Matches

59. The 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 

                   --------------------

What digit is represented by each letter ?

D should be 1 as we dont have D after that.
E > A

the possibilities for B and G are {4,2} {6,3}
(2,1 left out as D is 1 and 0,5 is left out as B is not 0)

the possibilities for C and E are {4,2} {6,3} or {0,5}

F is 11 - B or 10 - B so we have 5, 4, 6 as possible values

Assuming B and G is {6,3} and by trial and error we have


    12106

     5653

    ------

     6453

    ------

60.Fanta, Pepsi and Citra often eat dinner out.
a) Each orders either coffee or tea after dinner.
b) If Fanta orders coffee, then Pepsi orders the drink that Citra orders.
c) If Pepsi orders coffee, then Fanta orders the drink that Citra does not order.
d) If Citra orders tea, then Fanta orders the drink that Pepsi orders.

Which person/persons always orders the same drink after dinner ?

FANTA PEPSI CITRA
Coffee XXX XXX
XXX Coffee YYY
XXX XXX TEA

From the above table PEPSI cannot order TEA in condition 1
as CITRA will take TEA which would mean condition 3 fails.
So PEPSI orders Coffee and CITRA order TEA. so always
FANTA and PEPSI order the same drink.

61. On 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.
Find to which tribe each of them belongs, and the number of each of
their houses?

Adds No cannot be divisible by 12. otherwise we would have
Add 2nd statement and Evens 3rd statement true.

Even cannot be the all true guy as his 1st and 2nd are contradicting.
So Add says all truth.

From Evens 3rd statement we can say that he is the guy who is all lies.
because if thats true then we have Adds no also divisible by 12 contradicting.

So Add -- All True. Divide -- False True False. Even - All False.
From this we can see that
Add - 40
Divide - 37
Even - 27

Monday, June 28, 2004

46 - 51

46. There are 4 married couples out of which a group of 3
should be created. But in the group created there should
not be any couples? How many different ways are there.

To select the first person you have 8 choices.
To select the second person you have 6 choices leaving out the spouse.
To select the third person you have 4 choices.

Total ways of selecting is 8 * 6 * 4 / 3! = 32

47. Two men are walking towards each other along a rail track in the opposite
direction.One goods train crossed the first person in 20 sec.
After 10 min the train crossed the other person who is comming in
opposite direction in 18 sec .After the train has passed, when will
the two persons meet?

Let x be the speed of the train.
Let y be the speed of the person.
Let L be the length of the train.
Let Person A walk in the direction of train
Person B walks in the opposite direction.

L / (x-y) = 20 --1
L / (x+y) = 18 --2

From 1 and 2 we have (x+y)/(x-y) = 20/18.
x = 19y

Distance travelled by train in 10 mins = 190y
Distance travelled by Person A = 10y.
so total distance yet to be covered = 180y.
So total time remaing = 180y/2y = 90 minutes.

48. THERE ARE TWO PERSON EACH HAVING SAME AMOUNT OF MARBLES IN THE BEGINING
AND 1st PERSON GAINS 20 MORE FROM THE SECOND PERSON AND HE EVENTUALLY
LOSE TWO THIRDS OF IT DURING THE PLAY AND NOW THE SECOND PERSON HAS
4TIMES MARBLES OF WHAT FIRST PERSON IS HAVING NOW.FIND HOW MUCH MARBLES DID
EACH HAD IN THE BEGINING?

Let us assume X be the initial amount and the persons be A and B
A B
X X
X+20 X-20
(X+20)/3 X-20+(X+20)*2/3

X-20+(X+20)*2/3 = 4(X+20)/3
3X - 60 + 2X + 40 = 4X + 80
5X - 20 = 4X + 80
X = 100

49. THERE WERE TWO CLOCK ONE IS GETTING SLOW BY TWO MINUTES/HR AND
ANOTHER ONE IS GAINING 1 MINUTE EVERY HOUR AND EXACTLY AFTER HOW MANY HOURS
THERE TWO CLOCK HAS A 1HR DIFFERENCE?

Every Hour the Gain of the Faster clock over the slower one is 3 Minutes.
So to have 1 hour difference it will be 60/3 = 20 Hours

50. THERE IS A NUMBER WHICH WHEN ADDED WITH 33/4 GIVES THE SAME ANS AS
MULTIPLIED WITH 33/4

Let the no be X
X + 33/4 = X*33/4
4X + 33 = 33X
X = 33/29

51. Mr. T has a wrong weighing pan.One arm is lengthier than other.1
kilogram on left balances 8 melons on right.1 kilogram on right
balances 2 melons on left.If all melons are equal in weight,what is
the weight of a single melon?

Let the weight of the melons be X
Let the inbalance be W grams.

8X - W = 1.
2X + W = 1

solving we get X = 0.2 Kg

28 - 45

28. There is a safe with a 5 digit number as the key.
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.

65292

Couldnt find any proper method to solve except to trial and error.

29. Three friends divided some bullets equally. After all of them shot 4 bullets the total number of bullets remaining is equal to the bullets each had after division. Find the original number divided

Let initial be X bullets.

so each ones share is X/3.

each shot 4 bullets so we have (X - 12) = X / 3
X = 18

30. Father's age is three years more than three times the son's age. After three years, father's age will be ten years more than twice the son's age. What is the father's present age?

Let fathers age be X and sons age be Y

X = 3Y + 3
X + 3 = 2(Y + 3) + 10

solving we get X = 33 and Y = 10

31. How can 1000000000 be written as a product of two factors neither of them containing zeros
Ans: 2 power 9 x 5 power 9

Flicked the solution off the internet but this seems to be cool. :-)

32. Two 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 much faster is one train from other.

Distance travelled is same. Let total distance be D. Let meeting point be X kms.

Lets assume Train A travels from Bangalore to Mysore and Train B from Mysore to Bangalore.
Let S1 be speed of train A and S2 be speed of train B

so (D - X) / S1 = 1 hour.
X / S2 = 4 Hours.

Also D/ S1 - D/S2 = 3 hours.

Solving we get S1 is twice as fast as S2.

33. A man collects cigarette stubs and makes one full cigarette with every 8 stubs. If he gets 64 stubs how many full cigarettes can he smoke?

8 + 1 = 9.

34. Two trains start from stations A and B spaced 50kms apart at the same time and speed. As the trains start, a bird flies from one train towards the other and on reaching the second train, it flies back to the first train. This is repeated till the trains collide. If the speed of the trains is 25 km/h and that of the bird is 100km/h. How much did the bird travel till the collision.

The trains take 1 hour to collide. So the bird would have travelled 100 km as the speed of
the bird is 100 Kmph.

35. There are 6 volumes of books on a rack kept in order ( i.e. vol.1, vol. 2 and so on ). Give the position after the following changes were noticed.
1. Vol.5 was directly to the right of Vol.2
2. Vol.4 has Vol.6 to its left and both weren't at Vol.3's place
3. Vol.1 has Vol.3 on right and Vol.5 on left
4. An even numbered volume is at Vol.5's place
Find the order in which the books are kept now

251364

36. First : I have three children. The product of their ages is 36. If you sum their ages,
it is exactly same as my neighbor's door number on my left.
The second mathematician verifies the door number and says that it is not sufficient. Then the first says " Ok one more clue is that my youngest is really the youngest". Immediately the second mathematician answers. Can you answer the question asked by the first mathematician? What are the children ages?

36 can be split into 2 * 2 * 9 or 4 * 3 * 3 or 1 * 6 * 6
the second clue says the he has only one younger kid so that leave us 1 * 6 * 6

37. I bought a car with a peculiar 5 digit numbered license plate which on reading upside down could still be read. On reading upside down the value is increased by 78633.Whats the original number if
all digits were different?

0 1 6 8 9 are the nos which make sense when reading upside down.

Difference in the first and last digit is 7 and 3 so 8 and 1 fit the first and last digit.
second digit also has differnce of 3 so 0 and 6 fit the profile. so only left out is 9.

so origninal no is 10968

38. 9 cards are there. u have to arrange them in a 3*3 matrix.
cards are of 4 colors.they are red,yellow,blue,green.
conditions for arrangement: one red card must be in first row
or second row.2 green cards should be in 3rd column.Yellow
cards must be in the 3 corners only. Two blue cards must be in
the 2nd row. Atleast one green card in each row.

Total Color Condition
3 Green 2 cards should be on the third column and 1 card per row.
3 Yellow Cards in corners only.
2 Blue cards in 2nd row.
1 Red 1 or 2 row.

Y R G
B B G
Y G Y

39. 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

Let x be no of boys and y be no of girls.
x - 1 = y
2(y - 1) = x

solving we get x = 4 and y = 3

40. No. of animals (assume 4 legs) is 11 more than the no. of birds. If the
no. of birds were the no. of animals and no. of animals
were the no. of birds( ie., interchanging no.s of animals
and birds.), the total no. of legs get reduced by one fifth
(1/5). How many no. of birds and animals were there?

Let x be the no of animals and y be the no of birds.
x - y = 11
y*4 + x*2 = (x*4 + y*2) * 4 / 5

solving we get x = 22 and y = 11

41.


                   2 * *            |

                   3 * *            | No. 7 does not occur in this

             ----------------       |

                   5 * *            | multiplication.

                 * 4 *              |

               * * 3                | Find the product.

             ----------------       |

               * * * * *            |

             ----------------       |

Lets call the Nos multiplied A and B.
The last digit of B is 2 as we have the product step first no as 5.
The second digit of A should be greater than 5 as there is a carry forward.
The last digit of A is 1 as the product with B in step 3 gives the same.
The second digit of B is likely to be 3 or 4 as we have the product still a 3 digit no
and 2 digit > 5. so choosing 3 and 8 or 4 and 6 we can get the digit 4. but 4-6 leads
to 4 digit no so we have to choose 3 and 8. so the nos are
281 and 332.

42. TANVEER AND KUNAL WENT DOWN A DESCENDING ESCALATOR . THE ESCALATOR
WAS GOING DOWN AT A CONTANT SPEED . KUNAL WALKED DOWN THE STEPS AND
HAD TO COVER 50 STEPS TO REACH THE BOTTOM.TANVEER ON THE OTHER HAND , RAN
DOWN THE STEPS OF THE ESCALATOR AND HENCE HAD TO TAKE 75 STEPS TO REACH
THE BOTTOM . ACTUALLY , TANVEER TOOK 3 STEPS IN THE SAME TIME IT TOOK
KUNAL TO TAKE 1 STEP . HOW MANY STEPS WOULD BE visible when the ecalator
is stopped and not operating.?

Let X be the constant rate of the escalator.
Let N be the no of steps.
Time taken by kunal to come down = (N - 50)/ X
Time taken by tanveer to come = (N - 75)/ X
time taken by kunals one step = 3 * time taken by tanveers step.
(N - 50)/ 50X = 3 * (N - 75) / 75X
solving we get N = 100

43. Four perssons are three to cross a bridge they have one torch light
one person A can cross in 1 min
person B can cross in 2 min
person C can cross in 5 min
person D can cross in 10 min
They have to cross bridge with in 17 min.

At a time only two persons can cross
I A&B ----> 2
II A <----1
III C&D ---->10
IV B <----2
V A&B ---->2
__________
Total 17

44. Three are three boxes ,
In one box Two white balls
In two box 2 black balls
In three box 1 white &1 black
The lables on the boxes are not correct.Then you have to open
one box and to find the colour of the balls in all boxes.

Open the box labelled 1 white and 1 Black it has either black balls/ White balls
paste the label for that and switch the other 2.

45. A frog jumps 3 ft falls back 2ft in a day.how many days
will it take to come out of 30ft deep well?
First 27 days it gains 1 feet 28th day it climbs 3 feet coming out.

22 - 27

22. Ram Singh goes to his office in the city, every day from his suburban house.
His driver Gangaram drops him at the railway station in the morning and picks him up in the evening.
Every evening Ram Singh reaches the station at 5 O' Clock.
Gangaram also reaches at the same time.
One day Ram Singh started early from his office and came to the station at 4 O' Clock.
Not wanting to wait for the car he starts walking home. Mangaram starts at normal time, picks him up on the way and takes him back house, half an hour early.
How much time did Ram Singh walk?

Let X be the distance between the house and the station let D be the
distance walked by Ram Singh Let S be the speed of the car

so we have 2X/S = 2(X-D)/S + 30
so D/S = 15 Minutes. The car would have taken 15 mins to reach the station. So Ramsingh
walked for 45 Minutes.

23. In a railway station, there are two trains going.
One in the harbour line and one in the main line, each having a frequency of 10 minutes.
The main line service starts at 5 o'clock and the harbour line starts at 5.02A.M.
A man goes to the station every day to catch the first train that comes.
What is the probability of the man catching the main line train?

if he arrives between 5:00 and 5:02 he will take the harbor line train.
if he arrives between 5:02 and 5:10 he will take the main line train.

so probability = 8/10 = 0.8

24. A family X went for a vacation.
Unfortunately it rained for 13 days when they were there.
But whenever it rained in the mornings, they had clear afternoons and vice versa.
In all they enjoyed 11 mornings and 12 afternoons.
How many days did they stay there totally

Total no of non rainy days = (11 + 12 - 13)/2 = 5 days.
Total no of days = 13 + 5 = 18 days.

25. Albert and Fernandes have two leg swimming race.
Both start from opposite ends of the pool.
On the first leg, the boys pass each other at 18 m from the deep end of the pool.
During the second leg they pass at 10 m from the shallow end of the pool.
Both go at constant speed but one of them is faster.
Each boy rests for 4 seconds at the end of the first leg.
What is the length of the pool?

Let L be the length of the swimming pool.
Let S1,S2 be speed of Albert and Fernandez.

so (L-18)/S1 = 18/S2 -- 1
L/S1 + 4 + (L - 10)/S1 = L/S2 + 4 + 10 / S2
(2L -10) / S1 = (L + 10) / S2 -- 2

substituting S1/S2 from 1 and solving 2 we have
L^2 - 44L = 0 or L = 44 Meters

26. Every day a cyclist meets a train at a particular crossing.
The road is straight before the crossing and both are travelling in the same direction.
The cyclist travels with a speed of 10 Kmph.
One day the cyclist comes late by 25 min. and meets the train 5km before the crossing.
What is the speed of the train?

IF he would have come at the correct time he would be 10 * 25 / 60 = 25/6 Kms away from the crossing.
So the time taken by the bicycle to cross 5 - 25/6 Kms is the same as the time taken by the train
to cross 5 kms. So time taken by the boy to cross 5/6 kms is 5/60 hours. Speed of the train is
5 / (5/60) = 60 Kmph

27. Two twins have certain peculiar charcteristics.
One of them always lies on Monday, Wednesday, Friday.
The other always lies on Tuesdays, Thursdays and Saturdays.
On the other days they tell the truth. You are given a conversation.
Person A-- today is Sunday my name is Anil
Person B -- today is Tuesday, my name is Bill
What day is today?

Both of them speak truth on Sunday. So A cannot be true if B claims differnt.
so A is lying so he should be of type who lies on Tuesdays, Thursdays and Saturdays.
B is the guy who lies on Monday, Wednesday, Friday.
so the day is tuesday.

Sunday, June 27, 2004

16 - 21

16. 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

The no must be less than 250 and 0 is not zero so it has to be either
1 or 2. 8 and 2 satisfy the criteria the 4e = N and 4N = last digit e.
so one of the answer is 0 = 1, N = 8, E = 2, T = 7

17. Ann, Boobie, Cathy and Dave are at their monthly business meeting.
Their occupations are author, biologist, chemist and doctor, but not necessarily in that order.
1. Dave just told the biologist that Cathy was on her way with doughnuts.
2. Ann is sitting across from the doctor and next to the chemist.
3. 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

From 1 we have Ann or Boobie is the biologist.
From 2 we have Ann is neither a doctor nor a chemist.
From 1 & 2 we also have that Cathy is not a Doctor or Chemist.

Cathy is on her way so only 3 people are there so
Ann is the Biologist. Cathy is the Author.
Dave spoke so he is the chemist.
Boobie is the Doctor.

18.

N O O N
S O O N
+ M O O N
----------
J U N E
What is JUNE?

Since the result is 4 digit no we have to have N, S, M be less than 5 and J > 6.
3N <> N so N is not 5.
There is a carry forward in adding o so o should be greater than 3 also the carry forward
in adding o in both cases are different as U and N are different.starting with O = 4 and N = 2 we have
2 4 4 2
S 4 4 2
M 4 4 2
-----------
J 3 2 6

so S and M can be 1 or 5 and J should be 9. so JUNE = 9326.

19. here are 20 poles with a constant distance between each pole
A car takes 24 second to reach the 12th pole.
How much will it take to reach the last pole

Let C be the constant distance between the poles and S be speed of the car.
Distance to reach 12th pole is 11 * C
Time to reach 12th pole is 11 * C / S = 24
Time to reach 20th pole is 19 * C / S = ?

Time taken is 19 * 24 / 11 = 41.45 seconds

20. The minute and the hour hand of a watch meet every 65 minutes.
How much does the watch lose or gain time and by how much?

Let t be the time elapsed in minutes
(6 degrees) * t - (1/2 degree) * t = 360
t = 720 / 11 minutes.

The clock gains 5/11 minutes every hour.

21. There is a 4 inch cube painted on all sides.
This is cut down into of 1 inch cubes.
What is the no of cubes which have no pointed sides.

Total No of resulting Cubes 16. No painted sides leaving out
1 inch on all sides its 2 * 2 * 2 = 8 cubes.

Friday, June 25, 2004

12 - 15

12. The Bulls, Pacers, Lakers and Jazz ran for a contest.
Anup, Sujit, John made the following statements regarding results.
Anup said either Bulls or Jazz will definitely win
Sujit said he is confident that Bulls will not win
John said he is confident that neither Jazz nor Lakers will win
When the result cameit was found that only one of the above three had made a correct statement.
Who has made the correct statement and who has won the contest.

Bulls win will make Anup and John true
Jazz win will make Anup and Sujit true
Pacers win will make Sujit and John true
Lakers win will make Sujit true

Sujit made the correct statement. Lakers won the contest.

13. Everyday in his business a merchant had to weigh amounts from 1 kg to 121 kgs, to the nearest kg.
What are the minimum number of weight required and how heavy should they be?

The minimum number is 5 and they should weigh 1,3,9,27 and 81 kgs.

14. Four prisoners escape from a prison.
The prisoners, Mr East, Mr West, Mr South, Mr North head towards different directions after escaping.
The following information of their escape was supplied:
The escape routes were The North Road, South Road, East Road and West Road.
1.None of the prisoners took the road which was their namesake.
2.Mr.East did not take the South Road
3.Mr.West did not the South Road.
4.The West Road was not taken by Mr.East
What road did each of the prisoners take to make their escape?

A. From 1. 2. and 3. Mr North -> South Road
B. From A and 4 we have Mr.East -> North Road
From A and B Mr. West -> South Road and Mr. South -> West Road

15. There are six boxes containing 5 , 7 , 14 , 16 , 18 , 29 balls of either red or blue in colour.
ALL boxes contain only red balls or contain only blue.
One sales man sold one box out of them and then he says
" I have the same number of red balls left out as that of blue ".
Which box is the one he solds out ?

There are 3 bags containing odd no of balls and 3 bags containing even no of balls
so he should have sold a bag containing odd no of balls so 5, 7, 29 are the choices.
Total is 89 balls removing 5 we have 84 balls so split is 42 No way to split.
If removing 7 we again have no way to split 41 balls
so He should have sold the 29 balls bag.

9 - 11

9. A clock showing 6 o'clock takes 30 secs to strike 6 times.How long
will it take to strike 12 at midnight?

5 Intervals to strike 6 takes 30 seconds so time between the
strikes is 6 seconds. So to strike 12 it takes 11 intervals so will
take 11 * 6 = 66 seconds

10. There are 3 societies A,B,C having some tractors each.
A Gives B and C as many tractors as they already have.
After some days B gives A and C as many tractors as they have.
After some days C gives A and B as many tractors as they have.
Finally each has 24 tractors.what is the original No.of
tractors each had in the beginning

A B C
x y z
x-y-z 2y 2z A gives B and C
2(x-y-z) 2y-(x-y-z)-2z 4z B gives C and A
4(x-y-z) 2(-x+3y-z) 4z - 2(x-y-z) - (-x+3y-z)

so we have eqs
x-y-z = 6
-x+3y-z =12
-x - y + 7z = 24
also x + y + z = 3 * 24 could be used.

x = 39, y = 21, z = 12

11. A,B,C,D,E related.4 of them made these statements each.
i)C is my son in law's brother.
ii)B is my father's brother.
iii)E is my mother in law.
iv)A is my brother's wife.
who made these statements

E is the Mother in Law.
so she makes statement i)
B is the Son in Law A is his wife, C is his brother
C makes statement iv)
B make statement iii)
D makes statement ii) he/she is the child of C.

6 - 8

6. A says Party was held on :Thursday ,May 8th.
B says Party was held on :Tuesday,May 10th.
C says party was held on :Friday ,June 8th.
Given April 1 st was Tuesday. one of A,B,C says 1 correct, one says 1 wrong, and one was completely wrong of date,Month and day. Find the Day the party held.

Possible dates are and calculating from April 1st was Tuesday we
figure out that
Thursday May 8th
Saturday May 10th
Sunday Jun 8th
Tuesday Jun 10th.

Analysing this with the statements made by A, B, and C we see
that in case of A should have been completely wrong as May 8th is a Thursday we cannot say that it can be partially correct. B was wrong on month and C was Correct on Month. So the party date is Tuesday June 10th

7. A ship is away from the shore by 180 miles.A plane is travelling at
10 times speed of the ship which is moving away from the shore.
How far from the shore will they meet

(180 + x) / 10 = x

200 miles from shore

8. Every station in N railroad issue everyother station's ticket.
some stations are added.Now they have to issue 46 more tickets.
say the No.of stations after and before added.

Lets assume X is the no of new stations added so the no of tickets issued now is (N + X)(N + X -1)
Old tickets issued is N ( N - 1)
so No of additional Tickets is

(N + X)(N + X -1) - N ( N - 1) = 46
rearranging this is a quadratic

X^2 + (2N -1) X -46 = 0
since 46 is a product of 2 primes (2 and 23) and thats the only way to represent it we have 2N - 1 = 21 ie (23 and -2 are chosen
as we have to get -46) so N is 11 and solving X is 2 so the
answer is
No of Old Stations 11
No of New Stations 13

Thursday, June 24, 2004

1 - 5

1. amesh travels 760 km to his hometown partly by train and partly by car. He takes 8 hrs, if he travels 160 km by train and the rest by car. He takes 12 minutes more if he travels 240 km by train and rest by car. Find the speed of the car

80 Kmph

90 Kmph

100 Kmph

110 Kmph

Hint : Form equations
160/x + 600/y = 8 * 60
240/x + 520/y = 8 * 60 + 12
where x and y are speed of train and speed of car.

2. A six digit number is formed by the digits 1, 2, 3, 4, 5, 6 without repetition. What is the probability that the number formed is divisible by 4?

1/30

4/15

1/10

1/5

Hint: A number is divisible by 4 only if the last two digits are divisible by four. so list out all the favourable cases where the
last 2 digits are divisible by four divide by 6P2 (permutation
of selecting the last 2 digits from the given 6 digits)

3. Shyam has a basket of mangoes. He gives 1/3rd of the total number to his sister, 1/4th of the remaining to his brother and then 11, 16, 21 and 26 to his mother, father, uncle and aunt respectively. He eats one and finds the basket empty. How many did he have originally?

150

300

450

75

4. If in a particular number system 9 is written as 12, 14 as 20 and 49 as 100 what will 100 be represented as?

200

152

202

236

5. a, b, c, d and e are five consecutive even numbers. What is the maximum power of 2 by which the product of the above numbers be necessarily divisible?

6

7

8

9

Hint : out of the 5 consecutive even nos 2 will be divisible by 4