Question

Sum of digits of a 2-digit number is 9. If the difference between the number and the one obtained when the digits are exchanged is 45. The number is .

• A. 72
• B. 75
• C. 70
• D. 96

Answer 1

The correct option is A 72

Let the digit in the units place be y and digit in the tens place be x. Then, the number is 10x + y and the number obtained on reversing the digits is
10y + x.

From question, x + y = 9-------(1)
and
10x + y - (10y + x) = 45
$⟹$ 9x - 9y = 45
$⟹$x - y = 5---------(2)

On adding equations (1) and (2),
we get

2x = 14

$⟹$x = 7

On substituting x = 7 in equation (1), we get

7 + y = 9

$⟹$ y = 2

$\therefore$ The required number is 72.