Aptitude puzzles and Arithmetic Problems

1.There is a game which is being played by 2 persons A and B. The 2 players start the game keeping identical 50 paise coins on a blank board alternately. The 50 paise coins can be kept in the board such that no part of the coin is outside the board. It can touch the board edge but cannot protrude outside the board. The two players can place the coins anywhere on the board. The coins placed during the course of the game can touch each other at the periphery but cannot overlap with the already placed coins.
The player who has space to place the last coin is the winner i.e the player placing the last coin on the board with no space available for the opponent is the winner. If you are one of the players, what will your strategy be so that you definitely win?
Answer:-
1. I shall keep the 1st coin the exact centre of the board.
2. now after each coin that he keeps, I shall keep a coin exactly diagonally opposite. This shall reduce the space for his further attempts more than any other strategy.

2.Two guys A & B found out a old coin.on one side of that there is a picture of a king and on the other side it was written as 200B.C A told that the coin is a fake one but B said the other way. so who is right and why?

Answer:-
A is right. How would the coin maker know that there were 200 years left for Jesus to be born before he even existed?

3.A man had three daughters. Another man asked him the ages of his daughter. He told that the product of their ages is 36.
Second man was confused and asked for another clue. First man told him that the sum of their ages is equal to his house number.
Second man did some calculations and was still confused. He asked for another clue. First man told him that his youngest daughter had blue eyes. On hearing this, second man immediately gave the correct Answer.
Question : What are the ages of his daughter ?
Answer:-
Ages:1,6,6
Solution:-
To begin with, there is a small logical assumption that all the ages are integers.
4.Further to this, it is given that the product of the daughters' ages is 36. This gives the man just 8 possibilities:
AGE 1 AGE 2 AGE 3 SUM OF AGES
1 1 36 38
1 2 18 21
1 3 12 16
1 4 9 14
1 6 6 13
2 2 9 13
2 3 6 11
3 3 4 10
The correct solution has to exist within this range possibilities because the man could guess the same.
Calculation of the sum of their ages (the rightmost column) shows the only possible instances of the house no. If the sum were 38, 21, 16, 14, 11, or 10, he would have been able to guess the ages immediately. He was not able to do so only because the number of the house and the sum of the ages was 13! (This is because, even after this hint the solution was not unquely deducible…!!) Because of this, he did not have a unique solution until the man informed her about his youngest daughter.
It becomes clear that there is no ambiguity at this "youngest"position and that not two of them are tied at this position ( in case the ages would have been 9,2, and 2) . This is possible only if Kiran's daughters are 1, 6, and 6 years old.
With similar arguments, assuming no tie at the eldest position the correct set of ages would be 9, 2, 2.

5.Long back there was a king..
He had a very pretty daughter
He decided to hold a Svyamvar for his daughter
He called everyone but forgot to call a magician
Magician was very angry . He kidnapped the king's daughter.
King was very upset . He goes to the magician and pleads before him.
The magician , being soft at heart , tells the king that :
" O great King!! I agree to return your daughter back.
I 'll turn her into a flower and place her in your garden tomorrow morning.
You come there tomorrow morning.
If you are able to recognise her then I will return her back to u"
The next morning the king goes to his garden recognises his daughter and the magician returns her back to the king.
The question is how did the king recognise his daughter???
Some pts. to be noted:
1.The garden had all the species of flowers so the daughter was just like any other flower.
2. There are no tricks . The Answer is purely based on logic.
Solution:-
The king was very clever. When he heard that he "had" to recognise her daughter "flower" the next morniong, he decided to play a game with the magician. He went to the garden quitely late in the night and made some mark on all the flowers that existed there already. So when he came back to the garden the next morning, the task was cut out simple for him. He had to only look for a flower w/o that mark. And EUREKA...He found it.
What about all the flowers that Bloomed overnight? After marking all the flowers he also nipped all the Buds. This way he would be having a higher probability in identifying his daughter.

6.A man is trapped in a room.The room has 2 doors and 2 guards on those doors.One guard always speak true and the other always lie.Out of the two doors one goes towards escape and one towards jail. The man does not know which guard is lier and on which door and of course which door opens where. Fortunately,he has given a chance of escape by asking only one question to any of the guards.
Now the question is what question the man should ask?
Solution:-
Suppose the situation is
Gaurd 1 stands at Door 1 and Guard 2 stands at Door 2
The man should ask the Guard 1 this question -
" What will be the Answer of the Guard 2 when I ask him where does door 2 lead to?"
case 1:
If the Guard 1 Says "Guard 2 will say - towards JAIL" -
then the Door 2 will take him outside
Case 2:
If the Guard 1 Says "Guard 2 will say - towards outside" -
then the Door 1 will take him outside

7.A king has 100 sons(not dhritarashtra) and he wants a real fundoo girl to become his daughter-in-law. so he sets a plan. a certain amount is fixed for each son. (this much amount is to be given to the girl who marries that particular son). after that he invites a girl. the condition is that each son will be prsented to the girl and his amount will be told. you can choose any son randomly and after knowing the amount you can either accept or reject the guy. and go for another one, again randomly. but you can't go back to a previously rejected guy. the question is to get the maximum amount what will be your strategy?
The music stopped. She died. Explain
Answer:-
She was on LSS(Life Support System) and there was no UPS or power back up. The music stopped as the power went boom!
8. A man goes to a restaurant and orders Albatross Soup. The waiter brings the soup. The man tastes it, comes out of the restaurant and shoots himself. Why?
Reason: Albatross soup (variant 1.2 of 18 available across the globe) served in that hotel was extremely hot and poisonous. Got him all "fired" up. Didn't prolong the agony and shot himself.
9. A man wakes up in the morning, goes to a place, takes three left turns in succession and meets a masked man. What is the profession of the first man?
Profession: Good Samritan 4 times over.
Reason: The man had done 4 "right" turns (good deeds) the previous day so to make for the imbalance, he did 3 "left" turns and met his long lost friend Long Gone Silver whose face got burnt during the fire at the theatres on Friday the 13th, October 1999.
10.A Jailor has three bullets and he has four prisoners
The three of them are standing on the stairs one on first staircase second on second and the third on third& the fourth prisoner is made to sit in a closed room with no windows in proper security Jailor make the prisoners wear a cap,two of red colour & two of white He gave them a cap each No body knows about the colour of their cap neither can they see it
He declares that in his count for three if anyone of them will tell
the colour of his cap,he will spare him
You have to simply find that who is that lucky guy ???
Solution:-
i assume that the jailor will spare only the person who tells the colour of the cap first if he is right. also there is something worse than death to dissuade people from making false calls. and lastly that the lucky person is eager to get the ordeal over and if somebody knows the colour of his cap he will speak up immediately.
now under these assumptions:
the fourth person is helpless as he cannot see anything and due to the symmetry the replies do not give him any extra indicatons.
the third person sees two caps and if they are the same colour he speaks up immediately. now even the second person knows the colour of his cap as it is the same as the colour of the first persons cap, but unfortunately the lucky berth is gone.
if the first two are wearing different coloured caps the third is helpless and hence doesnot speak up. now the second person can infer the colour of his cap from the colour of the cap worn by the first person and speaks up and is spared.
so depending on the colours of the first two caps either the second or the third person is spared. now to determine the lucky guy we need the probablity of the first two guys getting a cap of the same colour which is 1/3, where as that they get different colour has 2/3 probablity and so the 2nd person could be called the luckiest if you wish!!
1. If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by
Ans: 330
2. The total no. of numbers that are divisible by 2 or 3 between 100 and 200(both inclusive) are
Ans:67
3. From a pack of cards Jack, Queen, King & ace are removed. Then the algebraic sum of rest of the cards is Ans:216
4. The average temperature of days from Monday to Wednesday is 37 degree Celsius and that of from Tuesday to Thursday is 34 degrees. The
temperature of Thursday is 4/5th of Monday. Then the temperature of Thursday is
Ans: 36 degrees
5. Swetha, Tina, Uma and Vidya are playing a gambling. In this different people lose in different games-in the reverse alphabetical order. The
rule is that if one loses she should double the amount of others. At the end of 4th game each of them have same amount of money (Rs.32). Which one of
them started with the least amount? (6) Which one of them started with the largest amount of money? (7.) At the end of the 2nd game what is the amount
of money with uma?
Ans: Vidya, Swetha, Rs.8
8. A cube of 12 mm is painted on all its side. If it is made up of small cubes of size 3mm. If the big cube is splitted into those small cubes,
the number of cubes that remain unpainted is
Ans: 8
9. B is 50% faster than A. If A starts at 9 A.M. and B starts at 10 A.M. A travels at a speed of 50 km/hr. If A and B are 300 kms apart, The time
when they meet when they travel in opposite direction is
Ans:12 noon
10. A graph will be there. Inside the graph sheet there will be a Quadrilateral. We have to count the number of squares in the Quadrilateral.
11. You are having 31kg of rice. You are provided with a 1kg stone for weighing. In how many weights the 31kg of rice can be weighed.
Ans: 5
12. A starts at 11:00AM and travels at a speed of 4km/hr. B starts at 1:00PM and travels at 1km/hr for the first 1hr and 2km/hr for the next hr
and so on. At what time they will meet each other.
13. There are 80 coins, among them one coin weighs less compared to other. You are given a physical balance to weigh. In how many wieghings the
odd coin can be found.
14. Dia of the circle 4cm. The shaded part is 1/3 of the square area. What is the side of the square.
Ans: root of 3pi
15. A,B,C, can do a work in 8,14,16 days respectively. A does the work for 2 days. B continues from it and finishes till 25% of the remaining
work. C finishes the remaining work. How many days would have taken to complete the work
16. Raja went to a beauty contest .his wife was eager to know the result he told that the lady wear a yellow sari was winner. Miss. Andhra
Pradesh Miss. Utter Pradesh, Miss. Maharashtra, Miss. West Bengal were the participants all the participants sat in a row. The conditions are (A) The
woman wore yellow sari won the competition. (B) Miss. West Bengal was neither the runner-up or winner.(C) Miss. West Bengal was not at either ends.(D)
Miss. Maharastra wore the white sari.(E) The women wore white sari and yellow sari sat at extreme ends.(F) The runner-up and winner did not sit
together. [This was the passage given and the questions were easy]
17. The ratio of white balls and black balls is 1:2. If 9 gray balls is added it becomes 2:4:3. Then what is number of black balls.
Ans:12
18. There are 10 coins. 6 coins showing head. And 4 showing tail. Each coin was randomly flipped (not tossed) seven times successively.after
flipping the coins are 5 heads 4 tails one is hided the hided coin will have what.
19. Two cars are 500 cm apart. each is moving forward for 100 cm at a velocity of 50 cm/s and receding back for 50 cm at 25 cm/s at what time
they will collide with each other.
20. People near the sea shore are leading a healthy life as they eat fish.but people at other part of the city are also healthy. Inference.
21. It is found from research that if u r a drunken then u have a less chance for chronic heart diseases. Inference.
22. A-B+c>A+B-C i) B is +ve, ii) B is –ve when it will hold true.
23. i) C.P is Rs 120 and profit is 30%
ii) C.P is Rs 210 and profit is 20%
we can find the S.P by using
i)only ii)only both i &ii neither i&ii
24. How will u find distance between Nagpur and Mumbai?
I took one hour more when I travel at 80 km/hr than at 90 km/hr.
25. 100 coins were collected by four persons each collected more than 10 each collected a different number each was an even number find what is
the max possible no of coins, two more questions based on the same passage.
26. A car travels from B at a speed of 20 km/hr. The bus travel starts from A at a time of 6 A.M. There is a bus for every half an hour interval.
The car starts at 12 noon. Each bus travels at a speed of 25 km/hr. Distance between A and B is 100 km. During its journey , The number of buses that
the car encounter is
27. The ratio of the ages of the father and the son is 5:3, After 10 years it will be in the ratio 3:2. What will be their ages.
28. There was a Island. In that Island there was Rubys and Emeralds. Those were available in plenty. 0.3 kg of ruby is 4 lakhs and 0.4 kg of
emeralds is 5 lakhs. Jayanth is buying 12 kg of Ruby and emerald. Choices will be given . Jayanth has to carry both ruby and emerald to the maximum
profit.
29. Varun buys 8 books,10 pens and 2 pencils and Babu buys 6 books, 5pens and 5 pencils. Babu pays 50% more than Varun. What is the amount Varun
spends in buying pencils.
30. Prakash and Revathi rent a fancy shop. Prakash imposes the following restrictions on Revathi for buying clips,stickers and lip sticks. The
number of clips is twice the no. of stickers. The no. of lipsticks should be more than the sum of clips and stickers. Cost of clip is 1 rupee. Cost of
lipstick is twice the clips. Cost of 1 lipstick is the cost of four stickers. Then What is the amount that Prakash spents for Revathi. Answer choices
will be given.
1.Three types of tea the a,b,c costs Rs. 95/kg,100/kg and70/kg respectively.
How many kgs of each should be blended to produce 100 kg of mixture worth Rs.90/kg,
given that the quntities of band c are equal
a)70,15,15
b)50,25,25
c)60,20,20
d)40,30,30

Ans: (b)

2.What is the maximum number of half-pint bottles of cream that can be filled with a 4-gallon can of cream (2 pt. =1 qt. and 4 qt. =1 gal)
A.16
B.24
C.30
D.64

Ans: D

3.There are two circles, one circle is inscribed and another circle is circumscribed over a square. What is the ratio of area of inner to outer
circle?
Ans: 1 : 2

4.In the following figure: A B C
D
E F G
H
I
Each of the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 is:
a)Represented by a different letter in the figure above.
b) Positioned in the figure above so that each of A + B + C,C + D +E,E + F + G, and G + H + I is equal to 13.
Which digit does E represent?

Ans: E is 4

5.There are 12 boys and 15 girls, How many different dancing groups can be formed with 2 boys and 3 girls.
48Which of the following fractions is less than 1/3
(a) 22/62
(b) 15/46
(c) 2/3
(d) 1

Ans: (b)

6.One of Mr. Horton,his wife,their son,and Mr. Horton's mother is a doctor and another is a lawyer.
a)If the doctor is younger than the lawyer, then the doctor and the lawyer are not blood relatives.
b)If the doctor is a woman, then the doctor and the lawyer are blood relatives.
c)If the lawyer is a man, then the doctor is a man.
Whose occupation you know?

Ans: Mr. Horton:he is the doctor.

7.A person wants to buy 3 paise and 5 paise stamps costing exactly one rupee. If he buys which of the following number of stamps he won't able to
buy 3 paise stamps.
Ans: 9

8.Mr. and Mrs. Aye and Mr. and Mrs. Bee competed in a chess tournament.Of the three games played:
a)In only the first game werethe two players married to each other.
b)The men won two games and the women won one game.
c)The Ayes won more games than the Bees.
d)Anyone who lost game did not play the subsequent game.
Who did not lose a game?

Ans:Mrs.Bee did not lose a game.

9.Two cars are 15 kms apart. One is turning at a speed of 50kmph and the other at 40kmph . How much time will it take for the two cars to meet?

Ans: 3/2 hours

10.Three piles of chips--pile I consists one chip, pile II consists of chips, and pile III consists of three chips--are to be used in game played by
Anita and Brinda.The game requires:
a)That each player in turn take only one chip or all chips from just one pile.
b)That the player who has to take the last chip loses.
c)That Anita now have her turn.
From which pile should Anita draw in order to win?

Ans:Pile II

11. 9.In a class composed of x girls and y boys what part of the class is composed of girls
A.y/(x + y)
B.x/xy
C.x/(x + y)
D.y/xy
Ans:C

12.One of the following is my secret word:AIM DUE MOD OAT TIE.With the list in front of you, if I were to tell you any one of my secret word,
then you would be able to tell me the number of vowels in my secret word.Which is my secret word?
Ans:TIE

13.If the operation,^ is defined by the equation x ^ y = 2x + y,what is the value of a in 2 ^ a = a ^ 3
A.0
B.1
C.-1
D.4
Ans:B

14.A coffee shop blends 2 kinds of coffee,putting in 2 parts of a 33p. a gm. grade to 1 part of a 24p. a gm.If the mixture is changed to 1 part
of the 33p. a gm. to 2 parts of the less expensive grade,how much will the shop save in blending 100 gms.
A.Rs.90
B.Rs.1.00
C.Rs.3.00
D.Rs.8.00

Ans:C

15.There are 200 questions on a 3 hr examination.Among these questions are 50 mathematics problems.It is suggested that twice as much time be
spent on each maths problem as for each other question.How many minutes should be spent on mathematics problems
A.36
B.72
C.60
D.100
Ans:B

16.In a group of 15,7 have studied Latin, 8 have studied Greek, and 3 have not studied either.How many of these studied both Latin and Greek
A.0 B.3 C.4 D.5
Ans.B

17.If 13 = 13w/(1-w) ,then (2w)2 =
A.1/4
B.1/2
C.1
D.2
Ans:C

18. If a and b are positive integers and (a-b)/3.5 = 4/7, then
(A) b < a
(B) b > a
(C) b = a
(D) b >= a
Ans: A

18. In june a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average
to 50% .How many games must the team have won in a row to attain this average?
A. 12
B. 20
C. 24
D. 30
Ans: C

19. M men agree to purchase a gift for Rs. D. If three men drop out how much more will each have to contribute towards the purchase of the gift/
A. D/(M-3)
B. MD/3
C. M/(D-3)
D. 3D/(M2-3M)
Ans: D

20. A company contracts to paint 3 houses. Mr.Brown can paint a house in 6 days while Mr.Black would take 8 days and Mr.Blue 12 days. After 8
days Mr.Brown goes on vacation and Mr. Black begins to work for a period of 6 days. How many days will it take Mr.Blue to complete the contract?
A. 7
B. 8
C. 11
D. 12
Ans:C
21. 2 hours after a freight train leaves Delhi a passenger train leaves the same station travelling in the same direction at an average speed of
16 km/hr. After travelling 4 hrs the passenger train overtakes the freight train. The average speed of the freight train was?
A. 30
B. 40
C.58
D. 60
Ans: B
22. If 9x-3y=12 and 3x-5y=7 then 6x-2y = ?
A.-5
B. 4
C. 2
D. 8
Ans: D

23. There are 5 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
Ans: 5c1/ 9c1

24. What is the selling price of a car? If the cost of the car is Rs.60 and a profit of 10% over selling price is earned
Ans: Rs 66/-

25. 1/3 of girls , 1/2 of boys go to canteen .What factor and total number of classmates go to canteen.
Ans: Cannot be determined.

26. The price of a product is reduced by 30% . By what percentage should it be increased to make it 100%
Ans: 42.857%

27. There is a square of side 6cm . A circle is inscribed inside the square. Find the ratio of the area of circle to square.
Ans: 11/14

28. There are two candles of equal lengths and of different thickness. The thicker one lasts of six hours. The thinner 2 hours less than the
thicker one. Ramesh lights the two candles at the same time. When he went to bed he saw the thicker one is twice the length of the thinner one. How
long ago did Ramesh light the two candles .
Ans: 3 hours.

29. If M/N = 6/5,then 3M+2N = ?

30. If p/q = 5/4 , then 2p+q= ?

31. If PQRST is a parallelogram what it the ratio of triangle PQS & parallelogram PQRST .
Ans: 1:2

32. The cost of an item is Rs 12.60. If the profit is 10% over selling price what is the selling price ?
Ans: Rs 13.86/-

33. There are 6 red shoes & 4 green shoes . If two of red shoes are drawn what is the probability of getting red shoes
Ans: 6c2/10c2

34. To 15 lts of water containing 20% alcohol, we add 5 lts of pure water. What is % alcohol.
Ans : 15%

35. A worker is paid Rs.20/- for a full days work. He works 1,1/3,2/3,1/8.3/4 days in a week. What is the total amount paid for that worker ?
Ans : 57.50

36. If the value of x lies between 0 & 1 which of the following is the largest?
(a) x
(b) x2
(c) -x
(d) 1/x

Ans : (d)

37. If the total distance of a journey is 120 km .If one goes by 60 kmph and comes back at 40kmph what is the average speed during the journey?
Ans: 48kmph

38. A school has 30% students from Maharashtra .Out of these 20% are Bombey students. Find the total percentage of Bombay?
Ans: 6%

39. An equilateral triangle of sides 3 inch each is given. How many equilateral triangles of side 1 inch can be formed from it?
Ans: 9

40. If A/B = 3/5,then 15A = ?
Ans : 9B

41. Each side of a rectangle is increased by 100% .By what percentage does the area increase?
Ans : 300%

42. Perimeter of the back wheel = 9 feet, front wheel = 7 feet on a certain distance, the front wheel gets 10 revolutions more than the back
wheel.What is the distance?
Ans : 315 feet.

43. Perimeter of front wheel =30, back wheel = 20. If front wheel revolves 240 times. How many revolutions will the back wheel take?
Ans: 360 times

44. 20% of a 6 litre solution and 60% of 4 litre solution are mixed. What percentage of the mixture of solution
Ans: 36%

45.City A's population is 68000, decreasing at a rate of 80 people per year. City B having population 42000 is increasing at a rate of 120 people per year. In how many years both the cities will have same population?
Ans: 130 years

A wizard named Nepo says "I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old." How old is Nepo?

Ans. 360 years old.

One dog tells the other that there are two dogs in front of me. The other one also shouts that he too had two behind him. How many are they?

Ans. Three.

A man ate 100 bananas in five days, each day eating 6 more than the previous day. How many bananas did he eat on the first day?

Ans. Eight.

If it takes five minutes to boil one egg, how long will it take to boil four eggs?

Ans. Five minutes.

The minute hand of a clock overtakes the hour hand at intervals of 64 minutes of correct time. How much a day does the clock gain or lose?

Ans. 32 8/11 minutes.

Solve for x and y: 1/x - 1/y = 1/3, 1/x2 + 1/y2 = 5/9.
Ans. x = 3/2 or -3 and y = 3 or -3/2.

Daal is now being sold at Rs. 20 a kg. During last month its rate was Rs. 16 per kg. By how much percent should a family reduce its consumption so as to keep the expenditure fixed?

Ans. 20 %.

Find the least value of 3x + 4y if x2y3 = 6.

Ans. 10.

Can you find out what day of the week was January 12, 1979?

Ans. Friday.

A garrison of 3300 men has provisions for 32 days, when given at a rate of 850 grams per head. At the end of 7 days a reinforcement arrives and it was found that now the provisions will last 8 days less, when given at the rate of 825 grams per head. How, many more men can it feed?
Ans. 1700 men.

From 5 different green balls, four different blue balls and three different red balls, how many combinations of balls can be chosen taking at least one green and one blue ball?

Ans. 3720.

Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled?

Ans. 167 minutes.

A person walking 5/6 of his usual rate is 40 minutes late. What is his usual time?

Ans. 3 hours 20 minutes.