Question

A 2-digit number is 3 times the sum of its digits. If 45 is added to the number, its digits are interchanged. The sum of digits of the number is

Answer 1

Let ones digit be x
tens digit be y

ATQ

Number=10x+y
After interchanging=10y+x

So
10x+y+45=10y+x
10x-x+y-10y= -45
9x-9y= -45
9(x-y)= -45
(x-y)= -45÷9
x-y=-5
x=-5+y

x+y=3{10x+y}
-5+y+y=30x+3y
-5+2y-3y=30x
-5-y=30x
-y-30x=5

sorry I can't solve after this
-(y+30x)=5

Answer 2

Answer:

Step-by-step explanation:

(x,y)=3(x+y)------------(1)

(x,y)+45=54

i.e, (x,y)=54-45=9

therefore,probable digits r (1,8),(2,7),(3,6),(4,5)..etc

among these,(2,7) is suitable.

so,9 is the answer.

verify:

          27+45=72.

or,     from(1),   27=3*(2+7)

                            =3*9

                            =27

hence verified.