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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 36 cless 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 cless 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 cless than the original number. Find the original number.
  1. Identify Units and Tens: 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 Digits: When the digits are reversed, the number becomes 10x+3x=13x10x + 3x = 13x. According to the problem, this reversed number is 3636 less than the original number. So, 31x−13x=3631x - 13x = 36.
  3. Simplify Equation: Simplify the equation: 18x=3618x = 36.
  4. Solve for x: Solve for x: x=3618=2x = \frac{36}{18} = 2.
  5. Find Tens Digit: Now, find the tens digit: 3x=3×2=63x = 3 \times 2 = 6.
  6. Final Original Number: The original number is 6262.

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