Question

the difference between the digits of a two digit number is 3. if digits are interchanged and the resulting number is added to original we get 143 . what was the original number .

Answer 1

Let the unit digit be x

Tens digit => x+3x+3

10(x+3)+x10(x+3)+x

digits interchanged =10x+x+3=10x+x+3

10(x+3)+x+10x+x+3=14310(x+3)+x+10x+x+3=143

=> 10x+30+12x+3=14310x+30+12x+3=143

=> 22x+33=14322x+33=143

22x=143−3322x=143−33

22x=11022x=110

x=11022x=11022

x=5x=5

Original number = 85

Answer 2

Let the unit digit be x and the tens digit be y (where y>x)
y-x = 3 ......(1)
Original number = 10y+x
According to the question
10y +x+10x+y =143
11y+11x =143
y+x= 13 .....(2)
Adding equation (1) and equation (2), we get
2y = 16
y =8
put the value of y =8 in equation (1)
8-x =3
-x =3-8
-x =-5
x=5
Original number = 10y+x= 10(8)+5=85