Question

A number consists of two digits whose sum is $8$. If $18$ is added to the number its digits gets interchanged. The number is?

• A. $53$
• B. $35$
• C. $92$
• D. $63$

Answer 1

The correct option is B $35$

Let one of the digit of the two digit number is $x$.

then problem other number is $(8-x)$

So,we get the equation

$10x+\left(8-x\right)+18=10\left(8-x\right)+x$

$10x+8-x+18=80-10x+x$

$9x+26=80-26$

$18x=54$

$x=\frac{54}{18}$

$x=3$

Then,

The digit in tens place is $3$

The digit in ones place is $(8-3=5)$, then the number is $35$ and when $18$

is added the result is $53$ the digits interchange their position in the new number.

Then,

We get the number is $35$

Option $B$ is correct answer.