Q7 of 25 Page 90

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.

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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