Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
What is the two-digit number? (SIDBI, 2006) I. The sum of the two digits of the number is 13. II. The number obtained by interchanging the two digits of the number is smaller than the original number by 45.
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
Let the ten's digit be $x$ and the unit's digit be $y$. Then, number $=10x+y$. I. $x+y=13 \Leftrightarrow y=(13-x)$. So, number $=10x+(13-x)$. II. $[10x+(13-x)]-[10(13-x)+x]=45 \Leftrightarrow (9x+13)-(130-9x)=45 \Leftrightarrow 18x=162 \Leftrightarrow x=9$. $y=13-x=13-9=4$. So, required number $=94$. Thus, both I and II together give the answer. ∴ The correct answer is (e).
Explanation as extracted from the printed page; notation may be imperfect.