Subject: General Aptitude · Chapter: Problems on Numbers · Exam: 2005 · Marks: · Difficulty:
If a number of two digits is $k$ times the sum of its digits, then the number formed by interchanging the digits is the sum of the digits multiplied by
(a)$k-1$
(b)$11-k$
(c)$9+k$
(d)$10-k$
Answer
Answer (as printed): B
Explanation
Let the ten's digit be $x$ and the unit's digit be $y$. Then, number $=10 x+y$. $$\therefore \quad 10 x+y=k(x+y) \quad \Rightarrow \quad k=\frac{10 x+y}{x+y} .$$Number formed by interchanging the digits $=10 y+x$. Let $10 y+x=h(x+y)$. Then, $h=\frac{10 y+x}{x+y}=\frac{11(x+y)-(10 x+y)}{x+y}$ $$=11-\frac{10 x+y}{x+y}=11-k .$$
Explanation as extracted from the printed page; notation may be imperfect.