Question

the sum of the digit of a two number is 11 .The number obtained interchange the digit exceeds the original number by 27 .find the number

Answer 1

let the two digit number be 10x+y
the number obtained by interchanging the digits is 10y+x
given,
sum of digits of two digit number is 11
I.e., x+y=11 --------eq 1
the number obtained interchange the digit exceeds the original number by 27
I.e., 10x+y+27=10y+x
10x+y+27=10y+x
10x+y+27-10y-x=0
9x-9y+27=0
9x-9y=-27
9(x-y) =-27
x-y=-27/9
x-y=-3 ------------eq 2
add eq 1 and eq 2
(x+y)+(x-y)=11+(-3)
x+y+x-y=11-3
2x=8
x=8/2
x=4
substitute x=4 in eq 1
therefore x+y=11
x+y=11
4+y=11
y=11-4
y=7
now substitute x=4 and y=7 in 10x+y
10x+y=10(4)+7
=40+7
=47
therefore the number is 47