The sum of the digits of a two-digit number is 12. The difference of the digits is 6. Find the number?

A. 93
B. 39
C. 75
D. 48
E. Either (a) or (b)

Explanation:

Let the two-digit number be 10a + b
a + b = 12 — (1)
If a>b, a – b = 6
If b>a, b – a = 6
If a – b = 6, adding it to equation (1), we get
2a = 18 => a =9
so b = 12 – a = 3
Number would be 93.
if b – a = 6, adding it to the equation (1), we get
2b = 18 => b = 9
a = 12 – b = 3.
Number would be 39.
There fore, Number would be 39 or 93.