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

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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

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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

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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.

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

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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

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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

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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.

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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.

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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

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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

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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

    ------    

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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.

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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

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

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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.

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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

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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

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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

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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