Question

Sum of the digits of a two-digit no. is 9.When we interchange the digits, it is found that the resulting new no. is greater than the original no. by 27. What is the two-digit no. ?

Answer 1

Let the digit in units place be x

digit in tens place = 9 - x

the number is 10(9-x)+x = 90 - 10x + x
= 90 - 9x ____(i)


when we interchange the digits ,

digit in units place = 9 - x
digit in tens place = x

the new number is 10(x)+9-x = 10x + 9 - x
= 9x + 9

given that if we interchange the digits, it is found that the resulting new no. is greater than the original no. by 27


so , the linear equation can be balanced as

90 - 9x = 9x + 9 + 27

90 - 9x = 9x + 36

90 - 36 = 9x + 9x

18x = 54

$x = \frac{54}{18}$

x = 3


so,

digit in units place = x = 3

digit in tens place = 9 - x = 9 -3 = 6

the number is 63



Note : It solely depends on the doer . the answer can be 36 also if initially , the tens digit is taken as x and units digit is 9 - x