Question

Sum of two digits of a two digit number is 9.When we interchange the digits,it is found that the resulting new number is greater than the original number by 27.What is the two digit number.Explain briefly

Answer 1

Sum of two digits of a two digit number is 9
Let the first digit be x
so, second digit =9-x
original number = x×10 +(9-x)
= 10x+9-x
=9x+9

When we interchange the digits
so,
another number =(9-x)×10+x
=90-10x+x
=90-9x

the resulting new number is greater than the original number by 27

90-9x=9x+9+27
90=9x+9x+36
90-36=18x
54=18x
54\18=x
3=x

original number=9x+9
=9×3+9
=27+9=36


another number =90-9x
=90-9×3
=90-27=63

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