Question

ab is a two digit number whose sum of the digits is 12 . The number obtained by subtracting ab from the number obtained after reversing the digits is 54. Find the number.

• A. 39
• B. 93
• C. 84
• D. 48

Answer 1

The correct option is A 39

Let the two digit number be ab = 10a + b and its reverse will be ba = 10b + a.
Now, ba - ab
= 10b + a - (10a + b)
= 10b + a - 10a - b
= 9b - 9a
= 9 (b - a)

Given 9 (b - a) = 54
$\Rightarrow$ b - a = 6
and b + a = 12 (given)
$\Rightarrow b+b+6=12$ (substituting value of a)
$\Rightarrow$ 2b = 18
$\Rightarrow$ b = 9
and a = 3

So, the number ab is 39.