Q. 74.3( 61 Votes )

The sum of the digits in a two-digits number is 9. The number obtained by interchanging the digits exceeds the original number by 27. Find the two-digit number.

Answer :

Let the unit digit be 'x'


Let the digit at ten's place be 'y'


The original number will be 10y + x


Given,


Sum of digits = 9


x + y = 9


x = 9 - y eq.[1]


Also,


If the digits are interchanged,


Reversed number will be = 10x + y


As, reversed number exceeds the original number by 27,


(10x + y) - (10y + x) = 27


10x + y - 10y - x = 27


9x - 9y = 27


x - y = 3


9 - y - y = 3 eq.[using 1]


-2y = -6


y = 3


Using this in eq.[1]


x = 9 - 3 = 6


Hence the original number is 10y + x = 10(3) + 6 = 30 + 6 = 36.

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