Subject: General Aptitude · Chapter: Problems on Numbers · Exam: 2006 · Marks: · Difficulty:
A two-digit number is 7 times the sum of its two digits. The number that is formed by reversing its digits is 18 less than the original number. What is the number?
(a)42
(b)52
(c)62
(d)72
Answer
Answer (as printed): A
Explanation
Let the ten's digit be $x$ and the unit's digit be $y$. Then, number $=10 x+y$. $$\therefore \quad 10 x+y=7(x+y) \Leftrightarrow 3 x=6 y \Leftrightarrow x=2 y .$$ Number formed by reversing the digits $=10 y+x$. $$\begin{aligned} & \therefore \quad(10 x+y)-(10 y+x)=18 \Leftrightarrow 9 x-9 y=18 \Leftrightarrow x-y \\ & =2 \Leftrightarrow 2 y-y=2 \Leftrightarrow y=2 . \end{aligned}$$ So, $x=2 y=4$. Hence, required number $=10 x+y=40+2=42$.
Explanation as extracted from the printed page; notation may be imperfect.