Solutions of Mathematical Puzzles -Shakuntala Devi

 Sum of the reciprocals

The sum of two numbers  is ten. Their product is twenty.Can you find the sum of the reciprocals of the two numbers?

   Solution: 

 Given :

a+b =10 ——-(1)

 ab=20——–(2)

      we need (1/a) +(1/b) =?

      It is simply obtained by dividing equation (1) by (2)

      We get  (1/a) +(1/b) =(10/20) => 1/2.

 

Find out the sum

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

Solution: 

                 Numbers divisible by 14 in range 100 and 1000 are 112 are

    112, 126,140,…….994.

   S= 112+126+……..+994.

   S= 14(8+9+……+71)

     = [(14)(8+71)(71-8+1)/2]

    =7(79)(64)

    =35392.

 

Read out the Figure

A London monument is marked as follows:

MDCLXVI

What year does it represent ?

 Solution: 

The given number is represented in Roman Numerals,

         In Roman Numerals Notation , we have 

         M=1000    D=500     C=100

         L=50            X=10       VI=6

        If we add all these together, the result is 1666.

 

Beetles and Spiders 

       Naval collected 8 spiders and beetles into a little box. When he counted the legs he found that there were altogether 54. How many beetles and how many spiders did he collect?

 Solution:

            Note:  Spiders have 8 legs and beetles have 6 legs.

      Use trail and error method.

  Assuming that only beetles are with the Naval , the no of legs will be 8 x 6 = 48 which is less than mentioned number of legs. Therefore 6 legs .We will reduce the no of beetles to 5 and number of 3 spiders.

  No. of Spiders = 3 and no of beetles = 5.

 

Value of  “S”

             S434S0 What number must be substituted with  ‘S’ to make it divisible by 36? 

  Solution: 

 If S434S0 is to be divisible by 36, then its also divisible by 4 and 9. To be divisible by        4, S S must be an even number.

      To be divisible by 4 and 9, sum of digits i.e 2S+11 is a multiple of 9.The  digit ‘8’ is              the only number that meets these two conditions.when we substitute ‘S’ with ‘*’              we get the number as 843480

Missing Terms 

48,60,58,72,68,104 …….

 

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

   Solution: 

               It is twin sequence, in which even placed numbers forms one sequence and odd placed numbers forms other sequence.

        48 , 58,68 , ?

     Next number is obatined by adding 10 to previous number. Therefore, 68+10 =78

       60,72,104,?

       Next number is obatined by adding 12to previous number. Therefore, 104+12=116

Therefore, next numbers are 78,116.

Angle of Hands

The time is 2:15 P.M.What is the angle between the hour and minute hands?

Solution :

θ= ( 11M/2  – 30 ) 

    Using the above formula with H=2 and M=15 , we get 

            = ( 165/2  – 60)

            =22.5°

Average speed

  It was a long drive. I drove 60 kilometres at 30 kilometres per hour and then an additional 60 kilometres at 50 kilometres per hour.

Solution: 

          Time required for  the first sixty kilometres = 120 minutes.

         Time required for  the second sixty kilometres =72 minutes.

         Total time required =120+72=192 minutes.

         Average Speed= (Total Distance Covered)/(Total Time taken)

                                   = 120/192

                                   =0.625 Km/minute

                                  =0.625 x 60 / hour

                                  =37.5 Km/hr

 Tell the Time

 Can you tell at what time between 7 and 8 O’clock, the two hands of a clock, will be in a straight line?

Solution:  

   Put θ=180° and find the time.

 

A problem of  Age 

Today was Lakshmi’s birthday.She turned 24.Lakshmi is twice as old as Ramu was when Lakshmi was old as old as Ramu now. How old is Ramu now?

Solution:

Age of Lakshmi now =24.

Laskshmiwa was x years when 24-x years ago.

   24-x years ago Ramu was x-(24-x) years old.

  Today she is x years old.

  24= 2(2x-24)

    Therefore, x=8.

 

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About Praveenkumar P Kalikeri

ABOUT US Hey,Thanks for dropping by .First I would like to Appreciate for your love towards the Mathematics Subject. My name is Praveenkumar Kalikeri. I'm an Engineering Student from Karnataka , India. My Passion for Mathematics , encouraged me to start this blog . I Started loving the Mathematics subject from my schooling days.I was greatly motivated by teachers, parents who always helped me .        Numbers have Beauty !! They fascinated me .. As we all know best method to try out something new is to study old theories , concepts , its drawbacks, etc. I ,myself Started learning Vedic Mathematics at age of 15. Here , I will share vedic maths tricks learned and modified by me in simple manner which will be useful in various competitive exams. "If You Believe , You Can Do".
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