51.This is a simple question. Don’t confuse. You have 12 gold coins of same weight except
one, which weighs less than others. You are given a balance machine but no weighing
measures. You can use the balance machine three times only. The balance machine tells
you just which side weighs more. How can you find the odd coin just by weighing the
52.Go through the previous question about gold coins. Because one of it is of less weight,
you may have solved it easily. But if one of it is of different weight (you don’t know
whether the odd coin is of more weight or less weight) then the question becomes more
complicated. Think whether you can solve it. If not, see the answer. If you are confused
with the answer also, then go to the next question and try to understand it and answer.
Revert back to this question again, to understand the technique. Don’t leave it frustrated.
53.A king wanted to present one gold toy of ten grams each, to every child in his kingdom.
He employed 100 artisans. Per day each artisan produced ten toys and hands them over to
the treasurer. After a month, the king knew that one of the artisans is cheating by
swindling 1 gram of gold per toy. Next day he went to the treasury in the evening when the
100 artisans brought their manufactured toys. The king has a weighing machine and
measuring stones. Using the machine only once, he was able to find the culprit. How?
54. Here is a riddle to test your reasoning skill. This can be done with a computer or
without it. Even a computer may take few minutes to answer. They say Ramanujam, the
mathematic wizard could calculate the answer in 10 minutes in computer-way. As told
earlier, there is another way of doing it. He could do it in few seconds in such a more
sensible way. Don’t rush for the answer. Think. Use your commonsense. A young girl was
walking towards a Shakti temple at 3 km per hour. Ram crossed her on a motorcycle at a
speed that is 20 times more than her. He wanted to give lift to her but could not dare. He
travelled for 3 minutes and on seeing temple of Shakti, he got courage and returned. He
saw her but was not courageous still. He returned back towards the temple, reached it and
again got inspired and returned. The process continued. In the final trip, he stood near the
temple and prayed Goddess Shakti “Please give me courage”. The girl, having reached the
temple, said from behind, “Shakthi the power… is not there in that stone. It is in you.
Discover it.” Now the question is: How much distance did Ram travel in total?
55. A had 5 chapattis, B had 3 and C had nil. They all ate equally and C paid 8/- to them as
the price for what he had eaten. How much A and B should get from the said amount?
Choose from the 4 answers: A5, B3 / A7, B1 / A4, B4 / none of these three.
56.Suppose a=b. With this equation, I will prove that a + b = b in four steps. Find out
where (in which step) I went wrong?
Step one: if a=b, then a²=ab.
Step two: Deduct b² from both: (a² – b²) = (ab – b²).
Step three: (a + b) (a – b) = b (a – b).
Step four: Deduct (a-b) from both: a + b= b. How is this possible? In which step lies the
57. Here is an excellent puzzle to test your reasoning skills. The five pandavas: Dharma
Raja, Bheema, Arjuna, Nakula and Sahadeva were sleeping in the Red-wax house and their
enemies burnt it. The pandavas were to escape through a tunnel. Only two people could go
through the tunnel at one time. Moreover, it was totally dark and without a torch they
could not proceed. They had only one torch. It means, two people should go out, and then
one had to take the lamp inside and accompany another one out. Total 4 trips. It would
take for Nakula and Sahadeva 5 minutes and Arjuna 10 minutes to come out. Bheema
would take 20 and Dharma 25 minutes respectively to come through the tunnel, as one
was hefty and another was old. This is an arithmetical problem and has no twists. How
much minimum time it would take?
58.In the above question, suppose they knew that the cave was going to collapse exactly in
60 minutes and they had to escape within the said time. If Nakula takes the responsibility
of bringing all the other four, it would take 75 minutes (if this is what you worked out in
previous question). But if you are more intelligent, there is a way to make it in 60 minutes.
59.If you are asked to find out the value of A (other than zero), when A+A= A x A, you
would answer that A = 2, as 2 + 2 = 2 x 2. Taking this as an example, find out the different
values of a, b, c, if a + b + c = a x b x c.
60.“Intellectual endurance” is the staying power, the capacity to persist without getting
distracted. At one point your brain ceases to cooperate, but please don’t stop doing this
calculation. Take a few minutes rest and start again. This is one way of developing
intellectual endurance. Take a ‘single digit number’ and a ‘three digit number’ of your
choice… For example, suppose the numbers are: 8 and 156, write down on a paper as 8-
156. Go on adding 13 to the first number and deduct 7 from the later. Do it simultaneously
(Here is the example. your first number is 8 – 156. Hence your second number would be
21-149, third 34-142). At the end… what are your final figures when you reach the single
digit answer on the right hand side? Don’t jump to calculate end figures, do it step by step
to test your patience.
61. From the following diagram choose the correct answer: 1) AB is lengthier than CD.
2) AB is shorter than CD. 3) AB is equal to CD.
62. A milkmaid adds 4 litres of water to 2 litres of milk before distribution. By mistake she
added 2 titres water to 4 litres of milk. How much more water has she to add to rectify her
63.A painter should mix 6 litres of paint, consisting of 4 litres of white and 2 litres of
black. But by mistake he mixed 2 litres of white and 4 litres of black. How much minimum
did he have to pour out to correct his mistake before adding the extra white paint?
64.What is “Two plus two by two?”
65.What is a plus b minus a plus b?
FOOD AND TRAVEL: These questions are to test your hyperactivity. Answer fast.
66.If 1 hen lays 1 egg in 1 day, how many eggs 2 hens lay in 2 days?
67. The question is an arithmetical question, not based on logic. If 4 hens lay 4 eggs in 4
days, how many eggs 2 hens lay in 2 days?
68.This is a logical question. How many eggs can a boy eat with empty stomach?
69.There are six eggs in the basket. Six people take each one of the eggs. One egg is left in
the basket. How could this be possible?
70.If two hens lay 2 eggs in 2 days, how many eggs does one hen lay in 1 day?
Arithmetically the answer would be “half-egg” which is not logical. Think of various
alternatives and give at least three logical probable answers for ‘one egg’.
71. A cook in a restaurant has a four minute hourglass, and a seven minute hourglass,
made of sand that shows the exact time. A customer orders a nine-minute egg. Using the
two glasses, how to cook exactly in the time given, not to a difference of even few seconds?
72.I take a private car from my house to my office located at the outskirts of the city in the
morning and back home in the evening. It costs me 300 rupees everyday. One day the taxi
driver informed me that there are two students who wish to go to their college every day in
the morning along with me! Their get-in point is exactly halfway between my house and
office. Their college is adjacent to my office. On the first day I told them, “If you tell me the
mathematically correct price that each one of you should pay for your portion of the trip, I
will let you travel free along with me.” How much should the individual student pay for
73. A passenger train starts at 5 p.m. from Agra and reaches Delhi at 10 p.m. From Delhi, a
train starts for every one hour throughout the day, at 5.30, 6.30 7.30 etc. How many such
trains would cross the passenger rail before it reaches Delhi?
74. The distance from Station to Bus-stand, Via Tank Bund is 8 miles. From Tank Bund to
Bus-stand via Station is 7 miles. From Station to Tank Bund via Bus-stand is 11 miles.
Calculate the distances between: 1. Station and Bus-stand, 2. Station and Tank Bund and
3. Bus-stand and Tank Bund.
75. There are some eggs in each bucket, named A, B, C, D, E. If A = 5; B+A =6; E+B =C;
E+C+B = 8, choose the values of A, B, C, D, E from 1, 2,3,4,5.
76.As in the same question above, find out the values of A, B, C, D, E from 1, 2,3,4,5 if D+B
= A+C; 2E =C+5; D+C = E. This is a more complicated question.
77. Three friends divide eggs from a bag equally. After each of them eat 4 eggs, the total
number of eggs remaining with them, is equal to 1/3 of total eggs. Find the original
number of total eggs.
78.You have two cups, one containing orange juice and one containing equal amount of
lemonade. One teaspoon of the orange juice is taken and mixed with the lemonade. Then a
teaspoon of this mixture is mixed back into the orange juice. Is there more lemonade in
the orange juice or more orange juice in the lemonade?
79.A student is studying for his examinations and the lights go off. It is around 1:00 AM.
He lights two uniform candles of equal length but one is thicker than the other. The thick
candle is supposed to last 6 hours and the thinner one illuminates for 4 hours. When he
finally goes to sleep, the length of the thick candle is twice longer than the thin one. For
how long does the student study in candle light?
80.There are 3 switches, 1, 2 and 3 in a hall in the ground floor. One of them is connected
to a dining room bulb in the third floor. You can’t see it from the ground floor, whether the
dining room light is on or off. How can you identify the correct switch? You can on and off
the switches as many times as you want, but you are supposed to go to the second floor
dining room only once and should announce the switch number from there.
81. A man decides to buy a horse for 600 rupees. After a year, he sells it for 700. He buys it
again for 800. And finally sells it for 900. What is his overall profit?
82.A swimmer jumps from a bridge into a canal and swims 1 kilometre against the stream.
There he passes a “floating cork” coming in opposite direction, going towards the bridge.
He continues swimming forward for half an hour more and then turns around and swims
back to the bridge. The swimmer and the cork arrive at the bridge at the same time. How
fast does the water in the canal flow?
83.Two cars (A and B) are travelling in opposite direction with 60 and 40 miles per hour.
The distance between them is 100 miles. A bird starts along with car A, and flies at a speed
of 80 miles per hour towards B. When it reaches car B, it turns back and when it reaches
the car A, again it turns to the opposite direction. What is the total distance that the bird
has travelled when the two cars met?
84.You drive at 20 mph from point A to B and return at 30 mph. what is the average
85.If you drive at 20 mph from point A to B, how fast must you drive back to attain an
average speed of 40 mph?