Question

The sum of digits of a two-digit number is 13. If the difference between the number and the one obtained when the digits are interchanged is 45, find the number.

• A. 94
• B. 49
• C. 85
• D. 76

Answer 1

The correct option is A 94

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, $x+y=13...\left(1\right)$

$10x+y-(10y+x)=45$

$\Rightarrow 9x-9y=45$

$\Rightarrow x-y=5....\left(2\right)$

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

$2x=18$

$\Rightarrow x=9$

On substituting $x=9$ in equation (1), we get

$9+y=13$

$\Rightarrow y=4$

$\therefore$The required number is 94.