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: Option D
Solution(By Examveda Team)
Let the ten's digit be x and the unit's digit be yThen, 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.
Related Questions on Problems on Numbers
If one-third of one-fourth of a number is 15, then three-tenth of that number is:
A. 35
B. 36
C. 45
D. 54
E. None of these
A. 9
B. 11
C. 13
D. 15
E. None of these
A. 3
B. 4
C. 9
D. Cannot be determined
E. None of these
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