Question

the sum of the digit of a two digit is 12 if the new number formed by reserving the digit is greater than the original number by 54 find the original number

Answer 1

let the original number be ab
then
a+b=12............
number formed by reversing its digits is ba
ba
then,according to given condition,
ba=ab+54
10b+a=10a+b+54
10b+a–10a–b=54
9b–9a=54
9(b–a)=54
9(b–a)/9=54/9
b–a=6
adding a+b=12 and b–a=6 we get
a+b+(b–a)=12+6
9a+b+b–a=18
2b=18
b=9
substituting. ...b=9in a+b=12
a+9=12
a=12–9
a=3
therefore..original number=ab=3