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The digit in the tens place of two-digit number is three times that in the units place. If the digits are reversed. the new number will be 35636 dess than the original number. Find the original number.

The digit in the tens place of two-digit number is three times that in the units place. If the digits are reversed. the new number will be 3636 dess than the original number. Find the original number.

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Full solution

Q. The digit in the tens place of two-digit number is three times that in the units place. If the digits are reversed. the new number will be 3636 dess than the original number. Find the original number.
  1. Identify units and tens digit: Let the units digit be xx. Then, the tens digit is 3x3x. The original number can be expressed as 10(3x)+x=30x+x=31x10(3x) + x = 30x + x = 31x.
  2. Reverse the digits: When the digits are reversed, the number becomes 10x+3x=13x10x + 3x = 13x.
  3. Set up equation for the difference: According to the problem, the original number is 3563635636 more than the reversed number. So, 31x−13x=3563631x - 13x = 35636.
  4. Simplify the equation: Simplify the equation: 18x=3563618x = 35636.
  5. Solve for x: Solve for x: x=3563618=1980x = \frac{35636}{18} = 1980.

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