Question : There is a number consisting of two digits, the digit in the unit place is twice that in the tens place and if 2 is subtracted from the sum of the digits, the difference is equal to $\frac{1}{6}$th of the number. The number is:
Option 1: 26
Option 2: 25
Option 3: 24
Option 4: 23
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Correct Answer: 24
Solution :
Let the tens digit be $x$.
Then, the unit digit is $2x$.
The number is given as $10x + 2x = 12x$.
According to the question,
⇒ $\frac{1}{6}\times 12x = x + 2x -2$
⇒ $2x=3x-2$
⇒ $3x-2x = 2$
$\therefore x=2$
The number is $12x=2 \times12 = 24$
Hence, the correct answer is 24.
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