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.
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
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
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
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