Question

The sum of a two-digit number and the number obtained by reversing the digits is 88. If the digits of the number differ by 2, find the numbers.

• A. 36, 63
• B. 53, 35
• C. 71, 17
• D. 44, 44

Answer 1

The correct option is B 53, 35

Let the ten’s and the unit’s digits in the first number be x and y, respectively.​

So, the first number $=10x+y$​

After the digits have been reversed, the second number will be $=x+10y$​

$(10x+y)+(10y+x)=88$​
$11x+11y=88$
$11(x+y)=88$​
$x+y=8$ ……….(1)​

Also given, the difference between the two digits is equal to 2. Therefore,

$x–y=2$ ………..(2)​

After elimination,​

$2x=10$ ​
$x=5$​
$2y=6$​
$y=3$​
The number is 53.​
The number reversed gives 35.​