The digit in the tens place of a two - digit number is three times that in the units place. If the digits are reversed, the new number will be 36 less than the original number. Find the original number. Check your solution.

Let the unit digit be y and tens digit is x so numbers = (10x + y), on reversing the digits number = (10y + x)


According to the question


x = 3y - (A)


And 10y + x + 36 = 10x + y


⇒ 10y - y + 36 = 10x - x


⇒ 9y - 9x = - 36


Putting (A) we get


9y – 27y = - 36


⇒ - 18y = - 36


⇒ y = 2


⇒ x = 3y = 6


So the number is 62


Checking the answer:


Digit at tens place = 6 = 3 × digit at unit place 6


Reversing the digits number becomes = 26


26 + 36 = 62


Hence, verified.


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