Question

If the digit in the unit's place of a two-digit number is halved and the digit in 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. 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

Represent the two-digit number as \(10x+y,\) where *x* is the tens digit and *y* is the units digit.

Halving the unit's digit and doubling the tens digit results in \(10(2x)+ \frac{y}{ 2}\).

This is equivalent to the number with the digits interchanged, which is 10y +x. Solving this equation reveals that the units digit is twice the tens digit.