Question

04.
A2 -digit number becomes four-sevenths of itsell
when the besitions of its digit are interchanged. The
difference between both digits is 3. what is the number?​

Answer 1

Answer :

63

Solution :

Let the tens digit and unit digit of the original numer be x and y respectively .

Thus ,

Original numer = 10x + y

After interchanging the digits , the tens digit and unit digit of new number will be y and x respectively .

Thus ,

New number = 10y + x

Now ,

According to the question , If the digits of original number are interchanged , then new number so obtained is 4/7th of the original numer .

Thus ,

=> New number = 4/7th of Original numer

=> 10y + x = (4/7)•(10x + y)

=> 7(10y + x) = 4(10x + y)

=> 70y + 7x = 40x + 4y

=> 40x + 4y - 7x - 70y = 0

=> 33x - 66y = 0

=> 33(x - 2y) = 0

=> x - 2y = 0

=> x = 2y --------(1)

Also ,

It is given that , the difference between the digits is 3 .

Thus ,

=> x - y = 3

=> x = 3 + y --------(2)

Comparing eq-(1) and (2) , we get ;

=> 2y = 3 + y

=> 2y - y = 3

=> y = 3

Now ,

Putting y = 3 in eq-(2) , we get ;

=> x = 3 + y

=> x = 3 + 3

=> x = 6

Hence ,

The required number is 63 .