Puzzles

Puzzles are dealt in a detailed manner with certain solutions.

Different puzzles are gathered from ShakuntalaDevi's puzzle books.

Keeping in mind certain puzzles for Infosys some reasoning problems are also dealt.

Puzzle name at the top of each problem will give a brief idea regarding the mode of application.

SELECTING A CANDIDATE

For  an advertisement of six local posts,twelve persons applied for the job.Can you tell in how  many different ways the selection can be made?

Solution:

        6^12

 

SET OF BAT AND BALL

When I wanted to buy a bat and ball ,the shopkeeper said they would together cost Rs.3.75.But I did not want to buy a  ball.The shopkeeper said that bat would cost 75paise more than the ball.What was the cost of bat and the ball?

Soluton:

        Given that bat and ball together cost Rs.3.75 = 375paise

        Let cost of the ball alone be x.

        Given cost of the bat is 75p greater than cost of the ball.

        So cost of the bat = x+75

        x+x+75 = 375

        2x = 375 – 75

        2x = 300

        x = 150p

        Hence cost of the ball = Rs.1.50

        =>Cost of the bat = 1.50 + 75 = Rs.2.25

 

 

PLAYING CHILDREN

A group of boys and girls are playing.15 boys leave.There remain 2 girls for each boy.Then 45 girls leave.There remain 5 boys for each girl.How many boys were in the orginal group?

Solution:

        Let B and G represent no.of boys and girls in the original group respectively.

        G ---------> 2

        B-15 ----------> 1

        G/B-15 = 2/1

        i.e., 2 girls are left for 15 boys who are alone.

        G-45 -------------------->1

        B-15 ------------------------->5

        5 boys are left out when 15 girls are alone.

         

        =>G/B-15=2/1    --------------------------------(1)

        =>G-45/B-15 =1/5   ----------------------------(2)

        (1) & (2) =>

        G = 2B-30

        5G – 225 = B - 15

        5 ( 2B – 30 ) = B – 15 + 225

        10B = B – 15 + 225 + 150

        9B = 360

        B = 40

        (1)=> G/40-15 = 2

        G=50 girls.

 

 

SOLVNG PROBLEMS

Reshma appeared for a maths exam.She was given 100 problems to solve.She tried to solve all of them correctly but some went wrong.But she scored 85.

Her score was calculated by subtracting two times th no.of wrong answers from the no.of correct answers.How many problems did Reshma do correctly?

Soluton:

        Assume  W as wrong answers and R as correct answers

        Given total no.of questions as 100

        R+W=100  ---------------------------(1)

        Score is calculated by subtracting 2 times wrong answers(2W)

        from right answers(R) and given as 85

        R-2W=85 -------------------------------(2)

        (2)-(1)

                       R-2W=85

                       R+W=100

                      ---------------------

                       W=5

        Hence,100-5=95 is the no.of correct answers  of Reshma.

 

       

A RUNNNG RACE

Sneha,Shilpa,Sushma join a running race.The distance is 1500 metres.Sneha beats Shilpa by 30 metres and Sushma by 100 metres.By how much could Shilpa beat Sushma over the full distance if they both ran as before?

Solution:

        Total distance covered by Sneha=1500m

                                 Shilpa=1500-30=1470

                                 Sneha =1500-100=1400

        Distance covered by Shilpa=1500*1400/1470=1428.6

        Distance to be covered by Shilpa to beat Sushma over full distance 1500-1428.6=71.4m

 

 

FILLING A CISTERN

Pipe S1 can fill a cistern in 2 hours and pipe S2 in 3 hours.Pipe S3 can empty it in 5 hours.Supposing all the pipes are turned on when the cistern is competely empty,how long will it take to fill?

Solution:

        S1 fills cistern in 1/2 hours

        S2 fills cistern in 1/3 hours

        S3 empties it in 1/5 hours

        A the pipes S1,S2,S3 working i.e.,filling the cistern

                         1/2+1/3-1/5=15+10-6/30=25-6/30=19/30

        No.of hours to fill=30/19=1 11\19hours.

 

 

SEQUENCE PROBLEMS

What are the next two terms in the sequence?1,1,5,17,61,217.................

Solution:

        The order in this cases is

        Tn=3*Tn-1 +2*Tn-2

            = 3(217)+2(61)

            = 773

        Tn+1=3(773)+2(271)

                     =2319+542

                     =2753

 

SEQUENCES

What are the next two terms in the sequence?

1,1,5,17,61,217.................

Solution:

        Tn=3Tn-1+2Tn-2

        =3(217)+2(61)

        =773

        Tn+1=3(773)+2(217)=2753

 

 

What are the next three terms to the series?

1+3+7+15+31+63...........

Solution:

        Actual term is 2exp n-1.

        The next three terms are:

        2exp7-1=127

        2exp8-1=255

        2exp9-1=511

 

 

A PROBLEM OF SHOPPING

Samsrita went out for shopping by taking with her Rs.15/- in one rupee notes and 20p coins.On return she had as many one rupee notes as she originally had and as many 20p coins as she had one rupee notes.She came back with 1/3rd with what she had.How much did Samsrita spend and how much did she take?

Solution:

        Let x be no.of rupee notes y be no.of 20pcoins.

        So,when going for shopping 100x+20y paise were there with Samsrita.

        On return she had 100y+20x paise.

        Also it is given that she had 1/3 rd of the orginal amount.

               1/3(10x+20y)=100y+20x

               =>4x=280y

               =>x=7y

               y=1 => x=7 total =7.20 <15

               y=2 =>x=14 total=14.40~=15

               y=3 =>x=21 total=21.60 >>15

        Hence the suitable value nearer to the amunt is 14.40 and so is the amount Samsrita carried with her.

               1/3(1440)=480paise.

        Rs.4.80/- is amount spent by Samsrita.

 

 

A PUZZLE OF CULTURAL GROUPS

Literary,Dramatic,Musical,Dancing and Painting are the 5 groups of a club.Literary group meets every other day,dramatic every third day,musical every fourth day,dancing every fifth day,painting every sixth day.Five groups meet on NewYears day of 1975 and starting from that day they met regularly on schedule.

How many times did all the 5 groups meet on same day in first quarter excluding Jan1,1975.How many days did none of them met?

Solution:

        LCM of 2,3,4,5,6 is 60.

        Hence excluding Jan1,1975 they met on every 61st day.
 

        60/2=30 60/3=20 60/4=15 60/5=12 60/6=10

        Literary meet for 30  2 day intervals.

        Dramatic meet for 20 3 day intervals.

        Musical meet for 15 4 day intervals.

        Dancing meet for 12 5 day intervals.

        Paintng meet for 10 6 day intervals.

        First quartr implies 3 months with 90 days.

        So inorder to a nswer that how many days do they don/t meet atleast once in first quarter is got by rounding all other categories.

By counting all the intervals for other groups no.of days in Jan 8,Feb 7,Mar 9.

        Total is 24.

 

 

STOLEN MANGOES

Three naughty boys stole some mangoes from a garden.Among them one counted and ate one.From the remainder he took precise third and went back to sleep.

After sometime second boy woke up,counted the mangoes,ate one,took an exact third of the remaining and went back to sleep.

After sometime third boy also did the same.In the morning they found one which was rotten and hence threw it away from the remainder,they made an exact division.How many mangoes did they steal?

Solution:
       

        Let the noof mangoes be x

        After the first boy had eaten noof mangoes =x-1

        After taking 1/3 rd of remaining it is 2x-2/3

        Second boy ate one and tok 1/3 then it is 2(2x-2/3 -1)=4x-10/9

        Third boy ate and tok 1/3 as 2(4x-19)/27=8x-38/27

        Deducting the rotten one from remaining noogf mangoes left=8x-38/27=8x-765/27

        This is divided among the three equally 8x-65/27=3n

               8x=81n+65

        Let n be equal to odd number 2b+1

               8x=81(2b+1)+65

               4x=81b+73

        Let b=2c+1

               4x=81(2c+1)+73

               2x=81c+77

        Let c=2d+1

               x=81d+79

        Least value of x for d=0 is 79

                        for d=1 is 160

                         for d=3 is 241

        On verfication,79-1=78/3=26

        Hence 79 is the correct answer.

 

 

AN ELECTION PROBLEM

My club had a problem recently.They had to appoint a Ssecretary from among the men and a joint secretary from among the women.

We have a membership of 12 men and 10 women.In how many ways can the selection be made?

Solution:

        As per the permutations and combinatins concept of mathematics,

        out of 12 men one selected as secretary can be done in 12c1 ways

        out of 10 women one selected as joint secretary can be done in 10c1 ways

        Hence one secrtary and one joint secretary is 12*10=120

 

 

SNAPPING A PLANE

A plane has a span of 12 metres.It was photographed as it was flying directly overhead with a camera with a depth of 12cm.In the photo the span of the plane was same.Can you tell how higher was the plane when it was snapped?

Solution:

        Actual span of the plane was 12m

        Span of the plane n photograph was 800m

        Depth of the plane is 12000m=12cm

        Hence,height of the plane when photographed be x

               12000:800 = x:12

               x=180m

 

 

A THRST PROBLEM

Pramatha and Pranathi went camping.They took their own water in bg plastic bottles.

Pramatha got thirsty and drank half the water in her bottle.A little later on she drank 1/3 f what was left.Sometime afterwards she drank 1/4 of what remained and so on

Pranathi also had a bottle of the same size.She drank half the bottle at the first instance ,half of what remained when she drank next and so on.

Aftr each took 10 drins ,the water Pramatha left was how many times greatr than the water Pranathi had left?

Soltuion:

        Pramatha for the first drink 1/2

                 for the second drink 1/3

                 for the third drink 1/4

        She drank 10 times and hence by the end of the 10th drink 1/11 of water she had in the bottle was over.

        Pranathi for the first drink 1/2

                 for the second drin 1/4

                 for the third drink 1/8

        So Pranathi as per the given information has drunk 1/1024 of water she had in the bottle.

        Water left for Pramatha/Water left for Pranathi=1/11 / 1/1024 =1024/11

 

 

NAME OF THE EXCHANGE

In GreatBritain some years ago the first threeletters of a telephone number usd to indicate  the name of the exchangeHow many such arrangements of 3 letters is it possible to devise from the 26 letters of the alphabet?

Solution:

For permutations the no.of ways to select is npr=n!/(n-r)!

Hence out of 26 letters the possible outcomes are 26p3=26!/23!=15600

 

 

VALUE OF THE SERIES

Take a good look at the following series.

1-1/3+1/5-1/7+1/9-1/11+1/13....................

Find the value of the series and multiply the answer by 4.You will notce that a well-known vale approximates this product.Even more interestng is that as you add more terms the approximation becomes closer.

Solution:

        Ths is an Arithmetic progresson with value .76 when two terms adde becomes .77 and multiplidd by 4 it becomes 3.04 and 3.08 repeatition it is 3.14 which pi value adjusted to 2 decimals.

 

 

PLANTING TREES

If you wished to plant some trees so that each was equidistant from every pther tree,what is the largest number you would plant?

Solution:

From the above informatin,as per equidstant formula of triangle,it is an equilateral triangle.

Planting at all the three corners only 3 can be planted.

The centroid is the middle point placed exactly equidistant from all the corners.

Hence 4 plants can be planted at euqidistant.

 

 

LENGTH OF A TRAIN

A train is travelling at the speed of 96 kmph.It takes 3 seconds to enter a tunnel and 30 seconds more to pass thorugh it completely.What is the length of the train and the tunnel?

Solution:

Speed of the train=95*5/18 m/sec

Time taken=3ssec

Length of the train=96*5/18*3=80m

Length of the tunnel=96*5/18*30=800m

 

 

A GAME OF BILLIARDS

Rajv,Sanjiv,Vinay were playing a game of Billiards.Rajiv can give Sanjiv 10 points in 50 and Sanjiv can give 10 points in 50.How many points in 50 must Rajiv gve Sanjiv to make an even game?

Solution:

        Rajiv   50      Sanjiv  40

        Sanjiv  50     Vinay   40

        Sanjiv  40      Vinay 40*40/50=32

        Rajiv 50       Sanjiv 40      Vinay 32

        Rajiv gains 18 points than Vinay (50-32=18)

 

 

WOMEN AT CLUB SOCIALS

Women outnumbered men by 16 at a club social.Seventimes the no.of women exceeds nine times the no.of men by 32.What was the number of men and women at club?

Solution:

        Let W and M be the  no.of women and men respectively.

        Given W=M+16.................(1)

             7W=9M+32................(2)

             7*(1)=>7W=7M+112........(3)

             (3)-(2) =>M=40

             W=56

 

 

FILLING WINE IN BARRELS

A friend of mine in London has a very nice cellar.He has two large barrels in the cellar.The larger barrel is mostly empty.But the smaller barrel is only 5/6 th full f wine while it can hold 536 litres.Supposing he empties the smaller barrel and fills the bigger barrel to find that the wine fills only 4/9 of it.How much wine would the larger barrel hold when full?

Solution:

5/6-------------------536

4/9-------------------?

5/6*536=4/9*x

=>x=1005 litrs

 

WEIGHT OF A BRICK

We have a brick of regular size.It weighs 4 kilograms.How much do you think asmaller brick four times small, but made of the same material weigh?

Solution:

        The weight of the given brick = 4 Kilograms = 4000 grams

        It is given that the smaller brick's volume is 4 times smaller than the given one.

        The volume of smaller brick = 4 * 4 * 4 = 64 times smaller

        The smaller brick's weight = 4000/64 = 62.5 grams

 

 

 A JUMPING FROG

A frog starts climbing a 30 ft wall. Each hour it climbs 3 ft and slips back 2. How many days does it take him to reach the top and get out?

Solution:

        Hours                                                Feets 

         1                                               3ft - 2ft = 1ft

         2                                               3ft - 2ft = 1ft

         3                                               3ft - 2ft = 1ft

         :                                                           :

         :                                                           :

        27                                              3ft - 2ft = 1 ft

      At the end of 27th hour the frog climbs 27fts and on 28th hour it climbs the remaining 3fts and comes out.

 

 

QUESTION OF PROBABILITY

My friend Parveen teaches at a school. One day she conducted a test for 3 of her students  and when they handed back the test papers, they had forgotten to write their names.

Parveen returned the papers to the students at random.What is the probability that none of the 3 students will get the right paper?

Solution:

        The possible combinations for the given condition are:

                  1         2          3            condition met

                  1         2          3                No

                  1         3          2              Yes

                  2         1          3                No

                  2         3          1                Yes

                  3         1          2                Yes

                  3         2          1                No

        The required probability = 2/6 = 1/3

 

 

MATHEMATICAL ODDITY

In  the 20th century there are only seven years whose numbers are a mathematical oddity because their numbers signify a prime number.The first one of its kind was the year 1951.Can you name the other sin?

Solution:

        1973,1979,1987,1993,1997,1999.

 

 

DOWN THE ESCALATOR

Recently,while in London,I decided to walk down the escalator of a tube station.I did some quick calculation in my mind.I found that if I wa down 26 steps, I require 30 seconds to reach the bottom.However ,if I am able to step down 34 stairs I would only require 18 secionds to get to the bottom.

If the time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom , can you yel the height of the stairway in steps?

Solution:

        Given that after walking 26 steps time needed to reach the bottom is       

        30 seconds  ---(1)
 

        Similarly after walking 34 steps, it needs

        18 seconds more to reach the bottom   ---(2)

        from (1) & (2) it is clear that

        for (34-26) steps it took (30-18) seconds.

        i.e; 12 seconds for 8 steps

        in 1 second --------?

        (1*8)/12=2/3 steps/sec.

        i.e; 2 steps in 3 seconds

        for  30 seconds -----------how many steps?

        => (30*2)/3=20 steps.

 Finally Total number of steps = 26 + (steps covered in 30 seconds)=26+20=46 steps.

 

A COMPUTING PROBLEM

Compute (100-1)(100-2)(100-3).........................(100+1)(100+2)(100+3)=?

Solution:

=>(100-1)(100-2)(100-3).........(100-100)(100+1)(100+2)(100+3)

=>(100-1)(100-2)(100-3).........(0)(100+1)(100+2)(100+3)

=0

 

 

A CIRCLE AND A TRIANGLE

What do you call a circle which passes through the vertices of of a triangle?

Solution:

Circumscribed.The meaning  to circumscribe is to describe a figure round another so as to touch it at points without cutting.This is  exactly what takes place with the circumscribed circle.

To find the center of such a circle,we have to bisect the sides of a triangle and errect perpendiculars  which are concurrent at the circumcentre.

The radius r of the circumscribed circle of the triangle ABC is given by

R=a/2SinA=b/2SinB=c/2Sinc

 

 

MISSING TERMS

48,60,58,72,68,104.......

Here is a sequenc.Can you find the two missing terms?

Solution:

The odd terms are in the decimal system and differ by 10.And each even term is the preceeding odd term expressed in the octonamy system.78-8=70,remainder 6:9:8=1,remainder 1.
Therefore the next two terms are: 78,116

 

 

PACKETS OF CANDY

If 6 men can pack 6 packets of candy in 6 minutes.How many are required to pack 60 packets in 60 minutes?

Solution:

Given  that for 6 men to pack 6packets of candy it takes 6 miutes.i.e., for 1 man to pack 1 packet it takes 1 miute.

Hence,for 60 packets to be packed in 60 miutes  we need 60 men.

 

 

A PROBLEM OF WEIGHT

In my neighbourhood lives a man who weighs 200 pounds.He has two sons.They both weigh 100 pounds each.On a festival day they decide to go across the river on a boat to vissit some relations.But the boat could carry a maximum load at only 200 pounds.Yes they managed to come across the river by boat.How did they?

Solution:

Let us assume that c1 ----------------->first son

                   c2 ---------------->second son

                    f ------------------>father

First the two sons c1,c2rowed across the river and c1 stayed behind while c2 returned in the boat to his father.
The son remained behind while the father crossed the river.
Then the other son brought back and the two brothers c1,c2 rowed over together.

 

 

A PROBLEM OF CANDY BARS

Recently I attended a birthday party.All the children in the party were given candy bars.All the children got 3 candy bars each except the child sitting in the end.She got only 2 candy bars.If only child had been given 2 candy bars there would have been 8 candy bars remaining.How many candy bars were there altogether to begin with?

Solution:

Suppose that there were x children at the party.

If we distribute the candies in the above mentioned ways,then the resulting expressions

        3(x-1)+2---------------------(1)

        2x+8-------------------------(2)

        3(x-1)+2=2x+8

        3x-3+2=2x+8

        3x-1=2x+8

        x=9

Therefore the no.of candies for distribution 2x+8=2*9+8=18+8=26

 

 

FIND OUT THE SUM

What is the sum of all numbers between 100 and 1000 which are divisible by 14?

Solution:

Let us assume that the sum is S

s=112+126+........+994

s=14(8+9+10+.....................+71)

s=14(8+71)(71-8+1)/2=7(79)(64)=35392

 

 

 

WALKING ALL THE WAY

One day I decided to walk all the way from Banglore to  Tumkur.I started exactly at noon and some one I know in Tumkur decided to walk all the way  from Tumkur to Banglore and she started exactly at 2 PM on the same day.

We met on  the Banglore  - Tumkur road at  5 past four and we both reached our destination at exactly the same time.At what time did we both arrive?

Solution:

         There fore Total time = 2:00 PM + 3:55 PM + 1:55 PM = 7:50PM

 

 

THE TRAINS AND THE FALCON

Two trains start from two opposite directions towards each other.The stations from which they start are 50 miles apart.Both the trains start at the same time towards the other train. As soon as it reaches the second one, it fies back to the first train and so on  and so forth. It continues to do so, flying bacwards and forwards from one train to other until the trains meet.

Both the trains travel at a speed of 25 miles per hour,and the bird flies at 100 miles per hour. How many miles will the falcon have flown before the trains meet?

Solution:

         The trains travel at 25 miles per hour.

Hence they will meet after travelling for one hour and the falcon also must have been flyingfor one hour. Since it travels at 100 miles per hour the bird must have flown 100 miles

 

 

VALUE OF 'S'

S434S0, what number must be substituted with to make it divisible by 36?

Solution:

        To be divisible by 36, the number has to be divided by 4 and 9

To be divisible by 4 , the number 'S' must be an even number and to be divisible by 9, the sum of all the digits of the number must be either equal to 9 or a multiple of 9

        i.e; S + 4 + 3 + 4 + S + 0 = 9n

        The only digit that meets these two condition is 8

 

 

HEIGHT OF A ROOM

Given the floor area of a room as 24 feet by 48 feet,and the space diagonal of the room as 56 feet,Can you find the height of the room?

Solution:

          We know that,

          Volume of a cube =l pow(2) + b pow(2) + h pow(2).

          Here the values of  l & b are given.

          We also know that

               (diagonal)pow(2)  = (length)pow(2) + (breadth)pow(2).

                 => (x)pow(2)    =  24 pow(2)  + 48 pow(2)

                 => x = 24squareroot(5);

          Therefore,volume= h pow(2) + x pow(2) =56 pow(2)

                 => h=16

            Therefore,height of the room=16 ft.

 

A QUESTION OF DISTANCE

It was a beautiful sunny morning. The air was fresh and a mild wind  was blowing against my wind screen I was driving from Banglore to  Brindavan Gardens. It took me 1 hour  and 30 miutes to complete  the journey.

After lunch  I returned to Banglore. I drove for 90 minutes.How do you explain it?

Solution:
     

        90 minutes = 1 hour 30 minutes.

        Hence,the driving time there and back is absolutely the same because 90 minutes and 1 hour and 30 minutes are one and the samething.


 

 

ARRANGE THE DIGITS:

Arrange the digits 1,2,3,4,5,6,7,8,9 in order from left to right and use only + or _ signs so as to produce a result of 100?

 

Sol:

        123-45-67+89

 

DIVISION OF 45:

Can you divide the number 45 into four parts such that when 2 is added to the first part, 2 is subtracted from the second part, 2 is multiplied by the third part, and the fourth part is divided by 2.All the four results to be the same number.

 

Sol:

     Let us take A,B,C,D are the four equal parts and their sum is equal to 45.

                A+B+C+D = 45

                Given that,

                A+2 = B-2 = C*2 = D/2 ----------------(1)

            =>A = B-4  ;  C = (B-2)/2  ;  D = 2(B-2)

            =>B-4 + [(B-2)/2] + 2(B-2) = 45

            =>B=12

               :. A=8 , C=5 , D=20

             And condition (1) is satisfied.

             i .e; 8+2 = 12-2 = 5*2 = 20/2

 

SPECIAL NUMBER:

What is the special about the number 1729?

 

Sol:

This is popularly known as Ramanujan's number. This is the known number that is a sum of two cubes in two different ways.

               i .e; (10*10*10) + (9*9*9) = 1729

                      ( 12*12*12) + (1*1*1) = 1729

 

 

PRICE OF A BOTTLE:

A bottle and its cork together cost Rs 1.10, and the bottle costs Rs 1.00 more than its cork. What is the price of the bottle?

 

Sol:

     Let us assume that,

              B = Price of the bottle

              C = Price of the cork

     It is given that,

              B + C = Rs 1.10 -------------------(1)

      and  B – C = Rs 1.00 -------------------(2)

     From the equations (1) and (2) it is clear that

            B = Rs 1.05

            C = Rs 0.05

 

A QUESTION OF DISTANCE:

It was a beautiful sunny morning. The air was fresh and a mild wind was blowing against my wind screen. I was driving from Banglore to Brindavan Gardens. It  took  me one hour and 30  minutes to complete the journey. After lunch I returned to banglore. I drove for 90 minutes. How do you explain it?

 

Sol:

    90 minutes = 1 hour 30 minutes.

Hence, the driving time there and back is absolutely same because 90 minutes and 1 hour 30 minutes are one and the same.

 

FOR THE CHARITIES:

One day when I was walking on the road in New Delhi, a group of boys approached me for donation for their poor boys' fund. I gave them a Rupee more than half the money I had in my purse. I must have walked a few more yards when a group of women approached me for donation, for an orphanage. I gave them 2 Rupees more than half the money I had in my purse. Then after a few yards I was approached by a religious group for a donation to the temple they were building. I gave them 3 Rupees more than half of what I had in my purse.

At last I returned to my hotel room, I found that I had only one Rupee remaining in my purse.

How much money did I have in my purse when I started?

 

Sol:

Suppose that the money in his purse when he started = x -------------------(1)

For poor boys fund he gave x/2 + 1 Rs/-  --------------------------------------(2)

     i .e; 1 Rupee more than half the amount he had.

   Now he left with [x - (x/2 + 1)] =(x-2)/2 Rs/-

   For Orphanage he gave [(x/2 – 1)/2] +2 = (x+6)/4 Rs/-  ----------------(3)

   Now he left with [(x-2)/2] – [(x+6)/4] = (x-10)/4 Rs/-

   For temple building he gave [(x-10)/4]/2 + 3  = (x+14)/8 Rs/-  ---------(4)

   Now he left with [(x-10)/4] – [(x+14)/8] = (x-34)/8 Rs/-

   Finally he had 1 Rupee in his purse.

   i .e; Actual amount – Expended amount = 1

   :. from (1),(2),(3) and (4) we have

   x-{ [ (x+2)/2 ] + [ (x+6)/4 ] + [ (x+14)/8 ] } = 1

   =>x-34=8

   => x=42

       :. The original amount in his purse at the beginning = Rs 42/-

 

 

A PAIR OF PALLINDROMES

Multiply 21978 by 4.Comment about the result?

Solution:

          21978*4=87912.

If we clearly observe the two numbers 21978 and 87912, the resultant number ie; 87912 is the reverse number of the number  219780.

There fore these two numbers are a pair of paindromes.

 

 

A COMPUTING PROBLEM

Compute:               [5-2/(4-5)]pow(2).

Solution:

         [5-2/(4-5)]pow(2)

        =[5-2/(-1)]pow(2)

        =[5+2]pow(2)=49.

 

 

CONTINUE THE SERIES

1,3,6,10.Name the next three numbers in the series.

Solution:

         The series is +2,+3,+4,-----------------

         There fore next three numbers are:

         10+5,10+5+6,10+5+6+7 = 15,21,28.

 

 

NAME FIVE TERMS OF ANOTHER SERIES

These are the numbers that are the first five terms of a series that add upto 150.Can  you name five terms of another series without fractons that add upto 153?

[ex: 10,20,30,40,50. sum=150.]

Solution:

Each term  in this series is a factorial, in other words,the product of a the numbers from 1 to that particular term considered.

The first five terms of the series are,there fore 1,2,6,24,120.

Their sum is 153 and are factorials of 1,2,3,4,5 respectively.

 

 

FIND OUT THE TIME

What does 1408 hours mean?

Solution:

         1408 hours  is actually 8 minutes past 2 PM.

         This is the system of twenty-four-hour cock.Writing the hours and minutes this way is a sensible means  of avoiding confusion between AM and PM.

 

 

FIND OUT TTHE PATTERN

What do you think the pattern is?   6,24,60,120,210,336,………………

Solution:

The series is   1.2.3, 2.3.4, 3.4.5, 4.5.6, 5.6.7, 6.7.8,----------

The next numbers would be 7.8.9,  8.9.10,-------

(or)  504, 720,-----------------------

 

 

THE TRAIN AND THE CYCLIST
 

A railway track runs parallel to a road until a bend brings the road to a level crossing. A cyclist rides along to work along the road every day at a constant speed of 12 miles per hour.

He normally meets a train that travels in the same direction at the crossing

One day he was late by 25 minutes and met the train 6 miles ahead of the level crossing. Can you figure out the speed of the train?

Solution:
 

     Suppose that the train and the cyclist meet everyday at the crossing at 8:00A.M. i. e; starts at 7:00A.M

     Since the cyclist is late by 25 minutes, he starts at 7:25A.M

     As his speed is 12 miles per hour, he reaches the crossing at

               7:25A.M + 1 Hour = 8:25A.M

     By 8:30A.M the train is 6 miles ahead of the cyclist

     The difference between their timings = 8:30A.M – 8:25A.M = 5 Minutes

     The difference between their distances = 6 Miles

     Therefore,the train travels 6 miles in 5 minutes

      In 1 minute it travels ---------------------?

               = [(1 * 6) /5] * 60

               = 72 Miles/hour

 

 

HEIGHT OF THE PALM TREE

A palm tree was 90 cm high, when it was planted. It grows by an equal number of cm each year, and at the end of the seventh year it was one ninth taller than at the end of the sixth year. Can you tell how tall was the tree at the end of the twelfth year?

Solution:

         Suppose that the tree grows x cm each year

         Height of the tree at the end of the sixth year = (90 + 6x) cm

         Growth in seventh year is,

         X = 1/9(90 + 6x) cm

         x = 10 + 2x/3

         x = 30

Therefore the height of the tree at the end of the twelfth year=(90+12*30)=450cm

 

 

PROBLEM OF AGE

Recently I attended a cocktail party. There was a beautiful young lady, who seemed very vitty and intelligent. She was posed a question, " how old are you? ".

She answered , " my age 3 years hence munltiply by 3 and from that subtracted

3 times my age 3 years ago will give you my exact age? How od is the lady?

Solution:

         Let the age be x

         Age after 3 years wi be (x + 3)

         Age before 3 years = (x – 3)

         Hence 3(x + 3) – 3(x – 3) = x

         x = 3x + 9 – 3x + 9

         x = 18

         Therefore the age of the lady = 18 years

 

CONSECUTIVE NATURASL NUMBERS

There are two consecutive natural numbers whose product is equal to the product of three consecutive natural numbers,for example x(x+1) = y(y+1)(y+2).What  are the two numbers?

Solution:

         14 * 15 = 5 * 6 * 7

 

 

SOME GLUTTON

A man sitting beside me at a hotel ate idlis one after the other by ordering plate by plate. He said to me after drinking some water the last one I ate was my hundredth idli in last five days. Each day  I ate 6 more than the previous day. Can  you tell me how many he ate yesterday?

Soluton:

        First day the number of idlis he ate be x

        Second day the count is (x+6)

        Third day ------------------------- (x+12)

        Fourth day ------------------------(x+18)

        Fifth day ---------------------------(x+24)

        Total is   5x + 6(1+2+3+4) =100

                   5x + 60 =100

                   x = 8

         Day                     Idlis

          1                         8

          2                        14

          3                        20

          4                        26

          5                        32

    So, on fourth day the number of idlis the man ate were 26.