Question

A number consists of two digits whose sum is $11$. If $27$ is added to the number, then the digits change their places. What is the number?

• A. $47$
• B. $65$
• C. $83$
• D. $92$

Answer 1

The correct option is A $47$

Let the ten's digit be $x$. Then, unit's digit $=(11-x)$.
So, number $=10x+(11-x)=9x+11$.
Therefore $(9x+11)+27=10(11-x)+x\iff 9x+38=110-9x\iff 18x=72\iff x=4$.
Thus, ten's digit $=4$ and unit's digit $=7$.
Hence, required number $=47$.