Question

If the digit in the unit's place of a two-digit number is halved and the digit in the tens' 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. Digits in the units place and the tens place are equal.
• B. Sum of digits is a two-digit number
• C. Digit is the units place is half of the digit in the tens place
• D. Digit in the unit's place is twice the digit in the tens place.

Answer 1

The correct option is D Digit in the unit's place is twice the digit in the tens place.

Suppose the two digit number is $10x+y$
Then, $10y+x=20x+\frac{y}{2}$
Or $20y+2x=40x+y$ or, $y=2x$
So, we see that digit at units place is twice the digit at tens place.