Question

If the sum of the digits of a two-digit number is 9 and the difference between the number and that formed by reversing the digits is 27, then the number can be

• A. 54
• B. 45
• C. 63
• D. 72

Answer 1

The correct option is C 63

Let the units digit be y and the tens digit be x.
Then, the number is of the form 10x + y.
By reversing the digits, the number will become 10y + x.
Given: x + y = 9 ..…(i)

( 10x + y) - (10y + x ) = 27
$\Rightarrow 9\times (-9y)=27$
$\Rightarrow$ x - y = 3
From (i) and (ii), we get
2x = 12
$\Rightarrow$ x = 6
Substituting the value of x in (i), we get, y = 3
Thus, the number is (10 × 6) + 3 = 63. Hence, the correct answer is option (3).