Question

(1) The sum of the digits of a two digit number is 12. If 18 is added to it, the digits are reversed. Find the number?
(2) The tens digit of a two digit number is three times the units digit. When the digits are reversed we get 36 less than the number. Find the original number?

Answer 1

let ones digit be = X
and tenth digit be = y
then number=. 10y+ x......................( 1 )
and x+ y= 12..............( given )
Now ,A.T.Q

10y+ x+18. =. 10x+y
10y-y. +x-10x. = -18
9y-9x=. -18
9(y-x)=. -18
y-x=. -2....................( 2 )


from ist and second, we get
x+y=12
-x+y=-2
--------------
2y=10
y=10/2=5


thus y=5
and we have.
x+ y = 12
x+ 5=12...............(putting y=5)
x= 12-5= 7
now x=7 and y=5
number= 10y+ x
10*5+7= 57
or
75