Subject: General Aptitude · Chapter: Problems on Numbers · Exam: 2005 · Marks: · Difficulty:
If the digit in the unit’s place of a two-digit number is halved and the digit in the ten’s place is doubled, the number thus obtained is equal to the number obtained by interchanging the digits. Which of the following is definitely true?
(a)Sum of the digits is a two-digit number.
(b)Digit in the unit’s place is half of the digit in the ten’s place.
(c)Digit in the unit’s place and the ten’s place are equal.
(d)Digit in the unit’s place is twice the digit in the ten’s place.
Answer
Answer (as printed): D
Explanation
Let the ten's digit be $x$ and the unit's digit be $y$. Then, number $=10x+y$. New number $=10\times2x+\frac{y}{2}=20x+\frac{y}{2}$. $\therefore 20x+\frac{y}{2}=10y+x \Rightarrow 40x+y=20y+2x \Rightarrow 38x=19y \Rightarrow y=2x$. So, the unit's digit is twice the ten's digit.
Explanation as extracted from the printed page; notation may be imperfect.