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What do you think? Sareen had three daughters Sudha, Seema and Reema—and their combined ages were half of hers. During the next five years Sonny was born and Mrs.
Sareen's age equalled the total of all her children's ages. After some years Kishu was born and then Sudha was as old as Reema and Sonny together. And now, the combined age of all the children is double Mrs. Sareen's age, which is, as a matter of fact, only equal to that of Sudha and Seema together. Sudha's age is also equal to that of the two sons.
What is the age of each one of them? The manager of the building told me that the building consisted of different kinds of apartments large and small.
Altogether the building contained apart- ments. Can you figure out how many apartments are there in eacb type, using round figures? The plate I got had a peculiar number on it. It consisted of 5 different numbers and by mistake when I fixed it upside down the number could be still read, but the value had increased by What was my actual license number? He bought two lathes to use in his workshop.
However, he found out afterwards that they did not serve the purpose for which he had bought them, and so he decided to sell them. He sold them each for Rs. Did he lose or gain in the transaction, and how much did each machine cost him?
I curiously noted that she just balanced against sixteen bricks, when these werefixedto the short end of the plank and I also noticed that if she were to fix them to the long end of the plank, she only needed eleven as balance. I wondered what was the girl's weight. The brick, I could guess weighed equal to a three quarter brick and three quarters of a pound.
If you were to close your eyes and pick them at ran- dom, how many marbles must you take out to be sure that there are at least two of one colour among the marbles picked out Can you find this number? How long will it taketo saw it into twelve equal pieces? He was fond of both the women and had no special preference for either. One lived near Churchgate and the other in Bandra.
He worked near a station midway between Churchgate and Bandra. After work he generally went to the station, and took whichever train got into the station first—Churchgate or Bandra. He arrived at whichever his destination it wast at random times, but found that be was visiting his Churchgate wife much more often than the other, despite the fact that both the Churchgate and Bandra trains were on schedules which brought him to hiS station equally often.
Since the same thing had been happening for a very long time, chance has been ruled out as the reason.
Can you find the reason for the frequency of his Churchgate trips? Our party consisted of 4 different professional groups, namely 25 writers, 20 doctors, 18 dentists and 12 bank employees. We spent altogether Rs. Later it was found that five writers spent as much as four doctors, that twelvedoctors spent as much as nine dentists, and that six dentists spent as much as eight bank employees. How much did each of the four professional groups spend? When I came put I found that I had just as many paise as I had rupees and half as many rupees as I had paise when I went in.
How much money did I have on me when I entered? I spent a few days in a small town, where I stayed as a paying guest with a British landlady. The heaters in the rooming house were all coin operated. One day my landlady requested my help in sorting out a problem. There were one hundred and twenty coins in her gas- meter and one of them, she knew, was counterfeit.
The counterfeit coin was either heavier or lighter than the others. Now the problem was to isolate this counterfeit coin and find out whether it was lighter or heavier, in five weighings. How can one do it? A certain container contains just one bacteria on the first day and there are twice as many on the next day. In this manner the number of bacteria in the container doubles itself everyday. Assuming that the container would be full of bacteria on the 10th day, on which day would the container be half full.
A man passing through the meadow one day saw Gopal grazing a number of sheep and in the course of a short cpnversation asked him how many of the grazing sheep were his own. Gopal's reply absolutely baffled him, which was as follows: Npw figure it out for yourself the number of sheep I own. They had agreed that whenever a player won a game he should double the money of each of the other players, in other words he was to give the players just as much money as they had already in their pockets.
In all they played seven games and, strangely, each won a game in turn in the order in which their names are given. But what was even more strange was that when they had finished the game each of the seven young men had exactly the same amount, Rs.
Can you find out how much money each person had with him before they began the game? So when he went around looking for a job as a farm-hand everyone refused to engage him, except farmer Gulab Singh, who was a very smart person. Gulab Singh engaged the services of Ram Rakhan at a salary of Rs. How- ever, he set a condition that he would forefeit Rs. Ram Rakhan accepted the job.
At the end of the month it was found that neither owed the other anything. This tought a lesson to Ram Rakhan. Can you tell jusf how many days Ram Rakhan worked and how many days he idled?
A group of match sticks is placed on the table and then it is reduced in turn by eachplayer by removing from the group at least 1 but not more than 4 match sticks. The player who takes the last match stick is the winner. If there is a group of 17 match sticks on the table how would you make your first move, if it was your turn and how would you continue to play to win?
And in 30 years the son will be half as old as his father. Bat they were so small that I made the vendor throw in two extra guavas for the samfe price. As I began to walk away thevendor mumbled that this transaction had made him lose 10 paise a dozen less the price we had settled. How many guavas did I get for my Rs. I bad Rs. Which 6 coins did I have? Can you find the year of the twentieth century which gives the greatest number of occasions of this kind?
She pushed a large circular table we have at home, into the corner of the room, so that it touched both walls and spilled a spot of ink on the extreme edge, and she said, 'Mummy here is a little puzzle for you. Look at that spot. It is exactly eight inches from one wall and nine inches from the other, Now tell me the diameter of the table without measuring it.. Can you? Can you cut the spade into three pieces that will fit to- gether and form a heart? Remember, no part of the material should be wasted.
Can you find the numbers? There are at least two solutions. Finally he decided to propose marriage to his beloved and invited her to travel towards his place and offered to meet her on route and bring her home.
The man is able to cover 4 miles per hour to the woman's 3 milesper hour. How far will each have travelled upon meeting? However, in some States the law permits a custo- mer to consume, after the deadline, what has been sold before the curfew.
In a certain bar 2 men ordered sufficient beer to cover their probable requirements in anticipation of the curfew. One man ordered and paid for 5 bottles and the other man ordered and paid for 3 bottles. But as the curfew sounded, an old friend of both the men approached and requested them to share with him the drinks. The two man agreed and shared the total eight bottles of beer bet- ween them. The friend thanked the two men and put down Rs.
How should this money be equitably divided between the two men? If you reverse my own age, the figures repre- sent my husband's age. He is of course senior to me and thedifference betweenour ages is one-eleventh of their sum. Can you find out the woman's age as well as her hus- band's age? The passenger train takes three times as long to pass the goods—even when they are going in the opposite directions. If the trains run at uniform speeds, how many times faster than the freight train is the passenger train moving?
He had altogether kilos of rice and he wanted to distribute the grain to people in such a manner that each old person received three kilos, each youiig person two and each child half a kilo. How many old persons, young persons and children were there? The square root of half the number of bees in a swarm has flown out upon a jasmine bush; eightninths of the whole swarm has remained behind; one female bee flies about a male that is buzzing within the lotus flower into which he was allured in the night by its sweet odour, but is now inprisoned in it.
Tell me the number of bees? Last time there was load shedding in Calcutta, I was readinga very interesting book and I could not stop. My neighbour Parveen gave me two candles and assured me that I could manage with them. Though the candles were of the same length, Parveen told me that one candle would burn for four hours and the other for five hours.
After I had been reading for some time 1 put the candles out as the lights came on again. And I noticed that what remained of one candle was exactly four times the length of what was left of the other.
Can you find out just how long those two candles were burning? Can you connect 12 of these dots with straight fees to form a perfect cross which has five dots iaaido it and 8 dots outside? Can you find out how many goats did the last man have, if 6 cows eat as much as 4 mules, and 10 goats as much as 3 cows? And how much did the first and second man each pay? But if there were no stream they could row it in seven minutes less than it takes them to drift down the stream. Can you say how long it would take them to row down with the stream?
Can you find the height of a steeple whose shadow at the same hour, is ft. I had two bottles containing 10 ounces of each. I poured just a quarter of an ounce of spirits into the water and shook them up. You can see clearly that the mixture was forty to one.
Now I thought that I should have the same quantity of fluid in both the bottles, and so I poured back a quarter of an ounce of the mixture into the bottle containing water.
It travels at the rate of one mile a minute through a tunnel which is also one mile long. Can you say how long it will take for the train to pus completely through the tunnel?
He also owns a pasture to graze them all. During a visit I asked two of the men to tell me their ages. One replied, 'One of our ages subtracted from tke other's equals What were their ages? Can you divide it into four pieces all of precisely the same size and shape?
These are the smallest possible numbers. Can you find the tfumbers? I have two 10 paise coins. A man and a woman always played against a man and a woman. However, no person ever played with or against any other person more than once.
They all played together in two courts on three successive days. Can you show how they could have done it? To quote an example three years ago a friend offered me a used typewriter for Rs. A year later he offered me the same for Rs. But I have decided to download it when he reduces next time. If he does a consistent reduction, at what price will he offer the typewriter to me next?
If I could have bought 4 more pineapples for Rs. What would be the price of each? I took the sections to a goldsmith and asked him to give me an estimate to join the 5 sections into a one piece necklace.
The goldsmith wanted Re. What is the cheapest method and how much should it cost me to get the five pieces joined together into one full necklace? Can you find the exact measurements for the sides of the boards? Demochares has lived one-fourth of his life as a boy, one-fifth 9s a youth, one-third as a man, and has spent thirteen years in his dotage. How old is Demochares? How old is Reena? If thecube is cut into 27 cubes of 1"x 1" x 1", how many 1" cubes do have any painted surfaces?
How many cigarettes can be made and smoked from 36 butts? One taxi driver I had the occasion to travel with was particularly lacking in courtesy, and so I asked for bis number. The driver gave me a sardonical smile and said, 'Well, if you divide my number by 2, 3, 4, 5 or 6 you will find there is always 1 remaining. But if you divide it by 11 there is no remainder. Do you want to know something more? There aren't no other cabby in this town with a lower number than—who can say the same,' and he drove off, while 1 stood there completely baffled.
What was the man's number? When they finally arrived, I had them cleared through the Customs and engaged three labourers to carry theip to my home 3 miles distant. As I was going to pay each of them equal amounts, they decided to carry a crate each equal distance. How did they manage to do it? Portchester" in London he was facing a serious problem pouring his wine from one vessel to the other.
Portchester had two ten quart containers full of wine. He also had a five quart and a four quart measure. All he wanted to do was put exactly three quarts into each of the two measures. He was standing there wondering how he is to do itl Now I offered to help and gave him some suggestions. Can you find out what was my suggestion, and how many manipulations of pouring from one vessel to the other did he require, without waste of any wine, tilting or other tricks. Can you draw four straight lines, the second beginning where the first ends, the third beginning where the second ends, and the fourth beginning where the third ends so that each dot is or at least one line?
If one-fifth of a hive of bees flew to the badamba flower, one-third flew to the slandbara, three times the difference of these two numbers flew to an arbour, and one bee continued to fly about, attracted on each side by the fragrant Ketaki and Malati, what was the number of bees?
If a player is eliminated as soon as he loses a match, how many matches are required to determine the winner? On the last day I did 51 miles, increasing my journey 4 miles each day. How many days did I travel and how far? How can these three, have each his own true Sabbath on the same day? He wanted the picture itself to occupy 72 square inches. What should be the smallest dimensions, the canvas he is going to obtain, should possess? The four sides of the garden are known to be 20, 16, 12 and 10 rods.
And it is also known that it has the greatest possible area for those sides. Can you find the area? The average price of the animals per head worked to Rs.
How many animals of each kind did he download? Before retiring they did some quick counting and found that the fruits were less than a hundred in number. During the night one thief awoke, counted the mangoes and found that he could divide the mangoes into three equal parts if he first took one for himself.
Shortly thereafter another thief awoke, counted the mangoes and he again found that if he took one Cor himself the loot could be divided into three equal parts. He ate up one mango, bagged J of.
The third thief also awoke after some time, did the same and went back to sleep. In the morning when they all woke up; and counted their mangoes, they found that the remaining mangoes again totalled 1 more than could be divided into three equal parts. How many mangoes did the boys steal? We exchanged our phone numbers and decided to meet each other soon. When she rang up and invited me to her house this is how she gave me the number of her hduse: Numbered on my side are the bouses one, two, three and so on.
All the numbers on one side of me add up exactly the same as all the numbers on the other side of me. I know there are more than fifty houses on that side of the street, but not so manyas five hundred. Can you find Stephaine's house number? There are an equal number of 25 paise coins, 50 paise coins and one rupee coins.
How many of each are there? The cube can be cut into 27 one inch cubes by the buzz-saw. Only 6 cuts of saw are necessary to do this, while keeping the pieces together. Now, can you reduce the number of cuts by rearranging the pieces after each cut?
If you can, how is it done? If you can't, why can't it be done? If they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other? Discussing the lease the land- lady told me: Now work it out for yourself and see how many years are there to gol How many years of unexpired lease did the property have?
Solutions The first brother is 70 inches tall, the second 72 the third 74 and the fourth brother 80 inches tall. Twenty-six minutes. Since the boys have as many brothers as sisters, there must be 1 boy more than the number of girls. If we try 2 and 1, 3 and 2, and 4 and 3, we will find that 4 boys and 3 girls is the solution to fulfil the requirement that each girl has twice as many brothers as sisters.
Naturally, the train travelling against the spin of the earth. This train will wear its wheels out more quickly, because the centrifugal force is less on this train. However, this represents the average of the 2 speeds and not the average speed for the whole trip. One'can think of different answers for this question, but yet thecorrect answer is very simple.
All we have to consider is that the shopowner could not have possibly lost more than the tourist actually stole. The tourist got away with the bicycle which cost the shopowner Rs. And this is the exact amount of the shopkeeper's loss. The lowest square number I can think of, contain- ing all the nine digits once and only once, is , the square of , and the highest square number under the.
By experiment'we find that the only numbers that can be turned upside down and still read as a number are 0, 1, 6, 8 and 9. The numbers 0, 1 and 8 remain 0, 1 and 8 when turned over, but 6 becomes 9 and 9 becomes 6. Therefore the possible numbers on the bus were 9, 16, 81, , or However, the number isthe only number which becomes a perfect square when turned over because is the perfect square of Therefore is the correct answer. Here is the formula that gives the minutes past twelve to which the hour hand points when the minute hand is exactly thirty minutes ahead.
The formula may be derived from the following: The Police Officer took thirty steps. In the same time'the thief took forty-eight, which added to his start of twenty-seven, carried fiim seventy-five steps. This distance would be exactly equal to thirty steps of the Police Officer. While striking 7 the clock strikes its first gong at 7 o'clock and it strikes 6 more at regular intervals. These 6 intervals take 7 seconds so that the inter- vals between gongs isiT seconds. In order that the little girl should have disposed of the oranges she had remaining after her second 97 Therefore, if 1 orange represents half of the remaining after the second sale, then she must have sold two oranges in her second sale, leaving the 3 oranges after the first sale.
All the transactions carried out through the counterfeit note are invalid, and therefore every- body stands in relation to his debtor just where he was before I picked up the note. A pound of cotton is heavier than a pound of gold because cotton is weighed by the avoirdupois pound, which consists of 16 ounces, whereas gold, being a precious metal is weighed by the troy pound which contains 12 ounces grams.
When Tinku takes 12, Rinku and Jojo will take 9 and 14 respectively—and then they would have taken altogether thirty-five nuts. Thirty-five is contained in twenty-two times which means all one has to do now is merely multiply 12, 9 and 14 by 22 to find that Tinku's share was , Rinku's and Jojo's Now as the total of their ages is 17i years or half Jayant was 24 and Mohini The minimum number of weights required is five and these should weight 1, 3, 9, 27 and 81 pounds.
Let's assume G is the number of glasses delivered intact. Let's assume B is the number of glasses broken. I don't know about you, but I would have handed over 5 two paise stamps, 30 one paise stamps and 7-fivepaise stamps. There isn't really any mystery, because the ex- planation is simple. While the two ways of selling are only identical, when the number of marbles sold at three for a paise and two for a paise is in the proportion of three to two.
There- fore when the first woman handed over 36 marbles and the second woman 24, they would have fetched 24 paise, immaterial of sold separately or at five for 2 paise. But if they each held the same number of marbles there would be a loss when sold together of 1 paise in every 60 marbles.
So, if they had 60 each, there would be a loss of 2 paise and if there were 90 each altogether they would lose 3 paise and so on. In the case of 60, the missing 1 paise arises from the fact that the 3 a paise woman gains 2 paise and the 2 a paise woman loses 3 paise. The couple arrived home 10 minutes earlier than ubual. Therefore the point at which they met Thus the wife should have been at that point at five minutes to six.
Since the man started to walk at five o'clock, he must have been walking for 55 minutes when hi met his wife. My aunt's share was Rs. We can build concentric hexagons' containing 1, 6, 12, 18, 24, 30, 36 and 42 circles.
When R '— becomes sufficiently large there will be room for extra circles. And the number of saucers that can be placed on the table is: If I walk 26 steps I require 30 seconds. If I walk 34 steps I require only 18 seconds. Multiplying the 30 by 34 and 26 by 18 we get and The difference between and is When we divide this number by the difference between 30 and , i.
It cannot be done. Each rectangle covers 1 white square and one black square, because on a chess board the white and black squares are always adjacent. The two squares which we remove from the chess board are of the samecolour, and so the remaining board has two more boxes of one colour than the other.
And after the rectangles have covered 60 boxes, there will be left two squares of the same colour. Obviously the remaining rectangle cannot cover these two squares. Just one look at the Dumber and we know that it cannot be a prime number. And if the problem has to have only one answer, this number can have only two factors. The factors are and , both of which are primes.
We know that each cat killed more mice than there were cats, and therefore the correct answer, clearly, is that cats killed mice. The forcwheel is 8 feet in circumference and the hind wheel 12 feet.
The entire mile was run in nine minutes. Though fr. And the last two quarters were run in two and a quarter minutes each. The clock broken in the manner shown in the illustration below: The numerals on each of the four parts will sum to The painted area as shown in the illustration below: Though it does not leave the clear area 4' x 4', however does measure 4' from top to bottom and from side to side.
We know that there were five droves with an equal number in each drove, and therefore the number must be divisible by 5. As every one of the eight dealers bought the same number of animals, the number must also be divisible by 8.
This leads us to the conclusion that the number must be a multiple of Now the highest possible multiple of 40 that will work will be found to be , and this number could be made up in one of two ways—1 cow, 23 sheep and 96 pigs or 3 cows, 8 sheep and pigs. But the first does not fit in because the animals consisted of 'Cows, Sheep and Pigs' and Therefore the second possibility is the correct answer.
Now, if the first frock usually sells for Rs. The second frock usually sells for Rs. Again I save Rs. The difference between the first frock and the second in terms of percentage gained is a little more than 2.
Hence the- second frock is a better download. The key to the solution is that with a little bit of pencil work, it will be found, while I can walk 5 miles, my friend who started from Tumkur can walk 7 miles.
Let's assume the distance between Bangalore and Tumkur is 24 miles, then the point of meeting would be 14 miles from Bangalore, and therefore I walked miles per hour while Let's assume that the man and the train normally met at the crossing at 8 A. But when the cyclist is late, he arrives at the bend at 8. Since the train takes 5 minutes to travel the six- milerun, the speed of the train is 72 m.
The woman made altogether Rs. She mads Rs. While the first was the example given, the top row must be one of the four following numbers: The manufacturer must take one flywheel made by each machine, find their total weight and compare this with the weight of the equivalent number of goodflywheelsto obtain the difference.
Then he must take 1 flywheel from machine number one, 2 flywheels from machine number The merchant must mix 70 Kilos of the Rs. I must have had Ri. If the sari cost Rs. A little thought indicates the sari costs Rs. So the difference in cost is Rs. The date on which I met the boy was 1st January , and the boys birthday was on 31st December, The boy was 11 years old on the day I met him. The whole brick weighs 3 lbs.
They had Rs. Let's assume that the age of the ship at present is X years and of the boiler Y years. Then The ship X is twice as old as its boiler Y—X was when the ship was x—X as old as the boiler is now. The following would be the procedure in chart form: Just myself! Only I was going to the market and I met all the others coming from the opposite direction.
They will never step out with right feet together. Three socks must be taken from the drawer, because if only two were taken one might be However, the third selection must result in a pair of white or brown socks. As Rekha's share falls in through her death, the farm has now to be divided only between Rashmi and Mala, in the proportion of one-third to one- fourth—that is in the proportion of four-twelfths to three-twelfths, which is the same as four to three.
Therefore Rashmi gets four-sevenths of the hundred acres and Mala three-sevenths. The man must have lost. And the longer he went on the more he would lose—with simple cal- culations, we can draw this conclusion: In two tosses he was left with three quarters of his money.
In six tosses with twenty-seven sixty-fourths of his money, and so on. Immaterial of the order of the wins and losses, he loses money, so long as their number is in the end equal.
Ten applicants had had neither mathematics nor literature training. So we can now concentrate on the remaining 90, applicants. Of the 90, twenty had had no mathematics and eight had had no literary training.
That leaves us with a remainder of 62 who have had training in both literature and mathematics. The method of working out this problem is to reverse the whole process—multiplying 2 by 10, deducting 8, squaring the result and so on. There were sixty eyes, so there must have been thirty animals. Now the question is what com- bination of four-legged pigs and two-legged ducks adding to thirty will give 86 feet.
With some pencil vork, we get the answer 13 pigs and 17 ducks. The simplest way isto find those numbers between 50 and , which are multiples of 2 and 3 leaving no remainder. These numbers are 54, 60, 66, 72, 78, 84, 90 and By scrutiny we find that if 78 is divided by 5 it will give 15 plus 3 left over. Therefore 78 is the total number of eggs Rasool had in his basket, before the accident. And therefore he was paid Rs. If 65 minutes be counted on the face of the same watch then the problem would be impossible.
The trains travel at 25 miles per hour. Therefore they will meet after travelling for one hour and the falcon also must have been flying for one hour. Since it travels at miles per hour, the bird must have flown miles. At a raise of Rs. Mammu had 5 marbles and NawaJ 7. Th6 ages must be as follows: Thus we can work out a table showing the number of each type apartment, which should look as follows: Type of Number of Rounded out to Apartment Apartments the nearest figu 2 8.
Now we only have to arrange these numbers so that when turned upside down the result will be larger by With some experiment we will find that the number is which is , inverted. He sold one for Rs. So he must have paid Rs. Therefore his total loss is Rs. A brick weighed 3 lbs. Therefore, 16 brickt weighed 48 lbs and 11 bricks 33 pounds.
Multi- plying 48 by 33 and taking the square root we get The girl's weight must have been about 39 79 pounds. In the first three pickings you may get 1 of each colour, on the 4th pick there must be at least two of one colour.
Therefore the answer is 4. The twelfth piece does not require sawing. The train schedule must have been in the follow- ing manner: Churcbgate train into the station at 1.
And Bandra train at 1. Churchgate train into the station at 1. This way each train would be arriving every ten minutes but his chances of getting the Churchgate train would be 9 times as great as of getting on the Bandra train, because if he arrives in the station between 1. The writers spent Rs.
Thus they spent altogether Rs. The five writers spent as much as four doctors, twelve doctors spent as much as nine dentists, and six dentists as much as eight bank employees. I must have entered the store with Rs. Let's assume P is a coin that's known to be perfect. The solution to this problem runs as follows: The container would be half full on the 9th day. Since the number of bacteria doubles each day, the container should be half full on the day before it became full.
Shepherd Gopal had one sheep only: A simple general solution to this problem would be as follows: Let's assume there are n number of players. Fakhruddin started with 15 quarter of a rupee pieces or Rs. Edward started with 29 quarter of a rupee pieces or Rs. Dev started with 57 quarter of a rupee pieces or Rs. Chunder started with quarter of a rupee pieces or Rs. Binoy started with quarter of a rupee pieces or Rs.
Arun started with quarter of a rupee pieces or Rs.