Question

sum of the digits of a two digit number is 7.when the digits are interchanged,the new number becomes as two more than twice the orginal number.find the orginal number

Answer 1

Let the unit digit be x
and ten's digit be y


then

Original number :- 10y + x

Reversed number :- 10x + y


◾ The sum of digit is 7

x + y = 7

x = 7 - y ........ ( i )


◽

10x + y = 2 + 2 ( 10y + x )

10x + y = 2 + 20y + 2x

10x - 2x + y - 20y = 2

8x - 19y = 2 .... ( ii )



Putting the value of x from ( i ) in ( ii )

8x - 19y = 2

8 ( 7 - y ) - 19y = 2

56 - 8y - 19y - 2 = 0

54 - 27y = 0

- 27y = - 54

y = 2


Putting the value of y in ( i )

x = 7 - y

x = 7 - 2

x = 5


So, the required number is :-

10y + x

10 × 2 + 5

= 20 + 5

= 25


So,

25 is the required two digit number!!


@Altaf