Question

A number between 30 and 70 has digits
which differ by 2 and the digits add to 12.
Find the number.

Answer 1

Let ones digit be x
And tens digit be y
So original no = 10×y+x
= 10y+x
Given
x-y = 2 (if x>y)....... (1)
y-x = 2 (if y>x) ........ (2)
x+y = 12.............. (3)

Adding (1) and (3)
x-y =2
x+y = 12
2x = 14
x = 7
Put in eq. (3)
7+y = 12
y = 5

Original no = 57
Now add (2) and (3)
y-x = 2
x+y = 12
2y = 14
y = 7
Put in eq. (3)
x+7 = 12
x = 5
So no is = 74
But it is not possible

Hence, original no is 57