Question

The sum of the digit of a two digit number is 10. If we reverse the digit the number will be 54 more than the original number.what is the original number

Answer 1

let the unit digit be x then tens digit be y.
Now the number=10y+x
sum of the digits=y+x=10
reversed number =10x+y
(10x+y)-54=10+10y+x
10x-x+y-10y=54
9x-9y=54
x-y=6
now adding eq 1 and 2
x+y=10
x-y=6
2x=16
x=8
then y=y+8 =10
=y. =10-8
=y. =2
original number =10 into 8+2
=82

Answer 2

tens digit = 10x
units =x
original no = 11x

units =10x
tens digit =10x
new no =20x

20x-54=11x
20x-11x =54
9x=54
x=54÷9
x=6

tens digit =60
units digit=6
the original no is 66