Puzzle Question- It Two Third of a number.........what is Number?

In last post you knew about what is Euclid’s Division or Lemma, Real Number, Part I, we shall continue this series later but right now I have to write a post about puzzle mathematics because I have been asked millions of time about puzzle or tricky mathematics so today I’m presenting some puzzling question.

Puzzle question: Mathematics is very interesting subject if you can understand and make it fun for you. But if not, it is boring. But don’t worry, today I bring some question answer from vast range of mathematics known as puzzling math. As you know that it is always point of discussion and judge someone’s iq. Here I present some puzzling and interesting question to you. Test it and take fun of it.

Problem 1:- Two third of a number is greater than three fifth of the number by 6. Find the number or what is number?

Answer:- Let the number be x

Than, 2/3 × x = 2x/3

Three fourth of the number = 3/5 of x = 3x/5

According to question, the given condition is

2x/3 – 3x/5 = 6

or 10x – 9x/15 = 6 

or    x   = 6 
     15

x = 15 x 6 =9

Hence the required number is 90. Answer

Puzzle question 2:- The sum of the digits of a two digit number is 12. The number formed by interchanging the digits is greater than the original number by 54. What is original number?

Answer- Let the unit digit of the original number be x

Then the tens digit of the original number = 12 – x

The original number is expended notation is

10 (12 – x) + 1 × x= 120 – 10a + x 

                         

                             = 120 + 9x

On interchanging the digits, the units digit is now = 12 – x

And the tens digit is now = x 

The number obtained by interchanging the digits, in expended notation

   

        = 10a + 1 × (12 – x) 

    

        = 10x + 12 – x

     

         = 9x + 12

Applying the given condition, 

  

The number obtained by interchanging the digit – original number = 54

ð          

9           x + 12 – (120 – 9x) = 54

ð   

             9x + 12 – 120 + 9x = 54

ð   

                          18x – 108 = 54

ð                                               

                           18x = 54 + 108 = 162

ð   

                               x = 162 / 18 = 9

The units digit of the required number = x = 9

The tens digit = 12 – x = 12 – 9 = 3

The original number = 39 answer

Puzzle Question 3. Five year ago, a man was seven times as old as his son. Five year hence, the father will be three times as old as his son. Find their present ages.

Solution:- Let five years ago, son’s age was x years.

Then, father’s age = 7x

Now, son’s present age is x + 5,

then father’s present age = (7x + 5)

Son’s age after five years = x + x + 5 = ( x + 10 ) years

Father’s age after five years = 7x + 5 + 5 + (7x + 10 ) years

According to the given condition,

Father’s age after five year = Three times son’s age after five years

ð                                            

                                 7x + 10 = 3 ( x + 10 )

ð    

                                 7x + 10 = 3x + 30

ð   

                                 7x – 3x = 30 – 10

ð 

                                                                                 4x = 20

ð   

                                           x  = 20/4 = 5

Therefore, son’s age five years ago = 5 years

Son’s present age = x + 5 = 5 + 5 = 10 years

Father’s present age = 7x + 5 = 7.5 + 5 = 35 + 5 = 40 years Ans

Problem 4. The present ages of Ishan and Raghaw are in the ratio 5:7. Four years later, their ages will be in the ratio 3:4. What is their present age?

Solution:-Let the present ages of Ishan and Raghav be 5x and 7x years respectively.

So, Ishan’s age after 4 years = (5x + 4)

       Raghav’s age after 4 years = (7x + 4)

According to question, the given condition is

                       

                      5x + 4 / 7x + 4 = 3 / 4

                        or 4,( 5x + 4) = 3 .( 7x + 4 )

                           or 20x + 16 = 21x + 12

                      or – 21x + 20 x = 12 – 16  =  – 4

                                    or - x = - 4

                                       or x = 4

Therefore, Ishan’s present age = 5x = 5 x 4 = 20 years

Raghav’s present age = 7x

 = 7 x 4 = 28 years.