Question

Sum of the digits of a two-digit number is 8.

When we interchange the digits, it is found that the resulting new number is greater than the original number by 36.

What is the two-digit number?​

Answer 1

Let number at tenth place be x

number = 10x

then number at ones place =8-x

original number = 10x + 8-x = 9x+8

after,

interchanging digits, we get new number = 10(8-x) +x

= 80-10x +x= 80-9x

A/q

(9x + 8) +36 = 80-9x

=> 9x + 9x =80 - 44

=> 18x = 36

or, x = 36/18=2

Now,

Original two digit number

= 9x+8=9*2+8

=26

Answer 2

Answer:

Let the digits at tens place and ones place: x and 9−x respectively.

∴ original number =10x+(9−x)

=9x+9

Now Interchange the digits: Digit at ones place and tens place: x and 9−x respectively.

∴ New number: 10(9−x)+x

=90−10x+x

=90−9x

AS per the question

New number = Original number +27

90−9x=9x+9+27

90−9x=9x+36

18x=54

x=

18

54

x=3

Digit at tens place ⇒3 and one's place : 6

∴ Two digit number: 36