Question

A two digit number is such that sum of its digit is $4$. If $18$ is added to the number it digits reversed. Find the number.

• A. $31$
• B. $13$
• C. $21$
• D. $41$

Answer 1

Answer: (B)

$13$

Let digit at ${10}^{\prime }s$ place $=A$, unit's place $=B$

$\therefore$ Number $=10A+B$

After adding $18$, it becomes $10B+A$

$\therefore 10A+B+18=10B+A$

$\therefore 9A+18=9B$ - (1)

We have $A+B=4$ (given)

$\therefore 9A+9B=36$

$\therefore 9A-36=-9B$ - (2)

Adding (1) & (2)

$18A-18=0$

$\therefore A=18,B=3$