Question

sum of the digits of a two-digit number is 9. When we interchange the digits it is found that the resulting number is greater than the original number by 27. What is the two digit number​

Answer 1

Let the number in the one's place be X and the number in the tens place be Y .
Number = 10 x Y + X
= 10Y + X = 9 ( By given condition ) ......i)
If we inter change the digits
New number :-
= 10 X + Y
B.G.C
= 10X + Y = 10 Y + X + 27
= 9X - 9 Y = 27
9 ( X - Y ) = 27
= X - Y = 3
X = 3+ Y
replace this value in equation i
10Y + X = 9
10 Y + 3+ Y = 9
11 Y = 9- 3
Y = 6 / 11
X = 3 + Y = 3 + (6 / 11 )= 39 /11
The number is 10 Y + X
= 60 / 11 + 39 / 11
=99 / 11 = 9
Hope this helps you.☺☺☺