Question

A number consists of two digits whose sum is $9$. If $27$ is added to the number, its digits are interchanged. Are the given steps to find the number true?
Step $1$: Let the unit's digit be x
Step $2$: Then, ten's digit $=(9-x)$
$\therefore$ number $=10\times (9-x)+x\Rightarrow 90-10x+x=(90-9x)$
Step $3$: Adding $27$ to the number $90-9x$ we get $117-9x$
Step $4$: Number with digits interchanged is $10x+(9-x)=9x+9$
Step $5$: $117-9x=9x+9$
Step $6$: Therefore unit's digit$=6$ and ten's digit $=3$
Step $7$: Hence the number $=36$.

• A. Yes
• B. No
• C. Cannot say
• D. Only step $1$ and $2$ are correct

Answer 1

The correct option is A Yes

All the given steps to find that unknown number are True.
Hence the option A is the correct answer.