Question

The sum of a $2$ digit number and the number obtained by reversing its digits is $154$. If the digits differ by $4$, find the number.

• A. $95$
• B. $73$
• C. $84$
• D. $62$

Answer 1

Answer: (A)

$95$

Let two digit number $=ab=10a+b$

Sum of number and reversed number $=154$

$(10a+b)+(10b+a)=154$

$a+b=14$

difference between digits$=|a-b|=4$

$a-b=\pm 4$

$(a+b=14)+(a-b=4)=2a=18$ $a=9,b=5$

$(a+b=14)-(a-b-4)=2a=10$ $a=5,b=9$

$\therefore \text{Number}=95\left(or\right)59$