Question : There is a number consisting of two digits. The digit in the unit's place is twice that of the ten's 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 digit at the tens's place and the digit at the unit's place be 'a' and 'b' respectively.
Given that b = 2a,
The number becomes 10a + b = 10a + 2a = 12a
Now, the sum of digits = (a + b) = (a + 2a) = 3a
According to the question,
3a – 2 = $\frac{1}{6}$ × (12a)
or, 3a – 2a = 2
or, a = 2
So, the number is 12 × 2 = 24
Hence, the correct answer is 24.
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