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

Let the two - digit number be 10a + b where a > b
According to the question,
a + b = 12 ..... (i)
a - b = 6 ..... (ii)
On adding equation (i) and (ii)
2a = 18
⇒ a = 9
From equation (i),
9 + b = 12
⇒ b = 12 - 9 = 3
∴ Number is 10a + b
= 9 × 10 + 3
= 93
∴ When a < b
Then required number is = 39