Question

A three digit number and is 459 more than sum of its digits. What is the sum of the 2 digit number ab and one digit a?

Answer 1

Let abc be the three digit number.
Given abc = a + b + c +459 .......(i)

Again abc=100a+10b+c...........(ii)

From equation(i) and (ii), we get

100a + 10 b + c = a + b + c + 459

100a - a + 10b - b + c - c =459

99a + 9 b = 459

9(11a + b) = 459
11a + b = 51 .....(iii)

To find: $ab+a=10a+b+a$
$=11a+b$
$\therefore ab+b=51$ [From equation(iii)]