In a two – digit number, the digit in the units place is twice that in the tens place and if two is subtracted from the sum of the digits, the result is equal to 1/6th of the number. What is the number?
Question
In a two – digit number, the digit in the units place is twice that in the tens place and if two is subtracted from the sum of the digits, the result is equal to 1/6th of the number. What is the number?
Solution
Sure, let's solve this step by step:
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Let's denote the digit in the tens place as x and the digit in the units place as 2x (since it's twice the tens digit). So, the number is 10x + 2x = 12x.
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The sum of the digits is x + 2x = 3x. If two is subtracted from this sum, we get 3x - 2.
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According to the problem, 3x - 2 is equal to 1/6th of the number, which is 1/6 * 12x = 2x.
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So, we have the equation 3x - 2 = 2x. Solving this equation gives x = 2.
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Substituting x = 2 into the number 12x gives the number 24.
So, the number is 24.
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