Question

A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, its digits are reversed. Find the number.

Answer 1

Let the digits be x and y.
Thus, number=10x+y
Now,
(10x+y) - 4(x+y)= 3.....(i)
and
(10x+y)+ 18=10y+x.....(ii)

Solving (i)
10x+y-4x-4y=3
or,6x-3y=3
or,2x-y=1....(1)
Solving (ii)
10x+y-10y-x=-18
or, 9y-9x=18
or,y-x=2...(2)

(1)+(2)
2x-y+y-x=1+2
or,x=3
Thus, y=x+2 (from (2))
y=5
Therefore the number= 10x+y=10x3+5=35