- Sum of the digits is a two-digit number
- Digit in the unit's place is half of the digit in the ten's place
- Digit in the unit's place and the ten's place are equal
- Digit in the unit's place is twice the digit in the ten's place
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Answer: Option 4
Let the ten's digit be x and the unit's digit be y Then, number = 10x + y New number : $$\eqalign{ & = 10 \times 2x + \frac{y}{2} \cr & = 20x + \frac{y}{2} \cr} $$ $$\eqalign{ & \therefore 20x + \frac{y}{2} = 10y + x \cr & \Leftrightarrow 40x + y = 20y + 2x \cr & \Leftrightarrow 38x = 19y \cr & \Leftrightarrow y = 2x \cr} $$ So, the unit's digit is twice the ten's digit.
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