Question

sum of the digits of a two digit number is 9 when we interchange the digit it is found that the resulting new number is great than the original number by27 what is the two digit number

Answer 1

A two digit number whose digits add up to 9 is x*10+9-x

adding 27 gives us the reversed digits:

So 10x+9-x+27=10(9-x)+x

9x + 36 = 90–9x

18x = 90–36 = 54

x = 3

So the numbers are 36 and 63
Hope it helps

Answer 2

let the tens difit be x

and the ones digit be y

x + y = 9 i)


10y + x = 10x + y + 27

9( x - y ) = - 27

x - y = -3 ii)


now by elimination method


x + y = 9
x - y = -3

x = 6


now putting the value of x in equation i)


x + y = 9

6 + y = 9

y = 3

then the number will be 63


I hope that my answer will help u