Question

The number obtained by interchanging the 2 digits of a 2 digit number is less than the original number by 54. If the sum of the 2 digits of the number is 12, then what is the original number?

• A. 28
• B. 39
• C. 82
• D. 23
• E. None of the above

Answer 1

The correct option is D 23

Let, required number = 10x + y
Where x > y
According to question,
(10x + y) - (10y + x) = 54
$\Rightarrow$ 9x - 9y = 54
$\Rightarrow$ 9 (x - y) = 54
$\Rightarrow$ x - y = 6 ........ (1)
and, x + y = 12 ........ (2)
From Equation (1) and (2),
$x-y=6$
$x+y=12$
$2x=18$
$x=9$
Value of x = 9, put in Equation (2)
$9+y=12y=12-9y=3$
$\therefore$ Number $=10\times 9+3=90+3=93$