Dear student,
Let x be the tens place digit and y be the unit place digit of a two digit number.
then, original number is =10x+y
from first condition
x+y=13 ----------(1)
from second condition ie, The number obtained by interchanging
its digits exceeds the given number by 9
So we can say,
10y+x=10x+y+9
=> x-10x+10y-y=9
=> -9x+9y=9
dividing by 9
=> -x+y=1 ----------(2)
adding equation (1 )and( 2)
we will get
2y=14
y=14÷2
y=7
putting y=7 in equation ----(1)
x+y=13
will be
x+7=13
x=13-7
x=6
original number=10x+y=10×6+7
=60+7=67
Hope you understood
Enjoy learning!!
Regards