Question

The sum of digits of a two-digit number is $13.$ If the number is subtracted from the one obtained by reversing the digits, the result is $45.$ Find the number.

• A. 94
• B. 49
• C. 85
• D. 76

Answer 1

The correct option is B: $49$

Let the digit in the unit's place be $y$ and digit in the ten's place be $x$

Original number $=10x+y$

When the digits are reversed, Reversed Number $=10y+x$

$\Rightarrow x+y=13$ ...(1) and

$10y+x-(10x+y)=45$ [Given: reversed Number - Original Number $=45$]

$\Rightarrow 9y-9x=45$ ....(2)

Multiply eq.(1) by 9 we get

$9x+9y=117$....(3)

Adding eq. (2) and (3)

$18y=162$

$\Rightarrow y=9$

Substitute $y=9$ in eq.(1)

$9+x=13$

$\Rightarrow x=4$

$\therefore$ The original number is $49.$