Question

The sum of a two-digit number and the nu​mber formed by interchanging the digits is 132. If 12 is added to the nu​mber, the new nu​mber beco​mes 5 ti​mes the su​m of the digits. Find the nu​mber. URGENT!!!

Answer 1

Let us assume x and y are the two digits of the two-digit number

Therefore, the two-digit number = 10x + y and reversed number = 10y + x

Given:

10x + y + 10y + x = 132
11x + 11y = 132
x + y = 12 ---------------1

Also given:

10x + y + 12 = 5 (x + y)
10x + y + 12 = 5x + 5y
4y - 5x = 12 ------------2

Multiply equation 1 by 5

5x + 5y = 60 ------------3

Adding equation 2 and equation 3

9y = 72
y = 8

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

The two digit number is = 10x + y = 10 * 4 + 8 = 48