Question

The sum of two digit number and the number obtained by reversing is 132.If 2 is added to number the new number becomes 5 times the sum of two digits. Find the number.

Answer 1

Let x: the 10s digit of the original number.
Let y: the 1s digit of the original number.

You are told that the sum of the original number and the number formed by swapping the digits is 132. so you can create the following equation:

(10x + y) + (10y + x) = 132

Simplifying this a little, we get:

11x + 11y = 132
11(x + y) = 132
x + y = 12

If 12 is added to the number (10x + y + 12), the new number is 5 x the sum of the digits (5(x + y)

So we have:

10x + y + 12 = 5(x + y)

Now let's simplify that.

10x + y + 12 = 5x + 5y
5x - 4y + 12 = 0

Now we have a system of two equations and two unknowns.

I'll set the first equation to x in terms of y, then substitute into the second.

x + y = 12
x = 12 - y

5x - 4y + 12 = 0
5(12 - y) - 4y + 12 = 0
60 - 5y - 4y + 12 = 0
72 - 9y = 0
72 = 9y
y = 8

Now that we know y, we can solve for x

x = 12 - y
x = 12 - 8
x = 4

We called x the 10s digit, so the original number is: 48