Question

a number consists of two digits whose sum is 9. if 9 is subtracted from the number its digits are interchanged. findthe number

Answer 1

Let the two digit number has X in ten's place and Y in unit place.


=> Number = 10X + Y



Given,

X + Y = 9 ------------(1)


On reversing the order of the digits , the number formed = 10Y + X.


Also given, 10X + Y - 9 = 10Y + X



=> 10X - X + Y - 10Y = 9


=> 9X - 9Y = 9


=> 9 ( X - Y ) = 9


=> X - Y = 1 ----------(2)


From (1) , we get


X + Y = 9


X = ( 9 - Y ) ----------(3)


Putting X = ( 9 - Y ) in equation (2),


X - Y = 1



9-Y - Y = 1

-2Y = -8


Y = 4.


Putting Y = 4 in equation (3),


X = ( 9 - Y ) = 9-4


X = 5.



Therefore , Required number = 10X + Y = 10 × 5 + 5 = 54.