Question

A two digit number is 3 more than 4 times the sum of its digits. if 18 is added to the number, it's digits are reversed. find the number

Answer 1

let the digit in ones place: x
let the digit in tens place: y

original number: 10y + x

when digits reversed, the number is: 10x+y

10y + x = 4(x+y) + 3
or, 10y + x - 4x - 4y = 3
or, 6y - 3x = 3
or, 2y - x = 1 --- (1)

(10y + x) + 18 = 10x + y
or, 18 = 10x + y - 10y - x
or, 9x - 9y = 18
or, 9(x - y) = 18
or, x - y = 2 ----(2)

(1) + (2)
= 2y - x = 1
x - y = 2
-----------------
y = 3


x - y = 2
or, x - 3 = 2
or, x = 5

10y + x
= 10.3 + 5
= 35

The two digit number is 35