The digit in the tens place of a two - digit number is three times that in the unit’s place. If the digits are reversed, the new number will be 36 less than the original number. Find the original number and choose the option representing the same.

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Detailed Solution

It is given that the digit at the tens place is three times the digit at the unit’s place and if the digits are reversed, then the new number formed is 36 less than the original number.
Any two-digit number is expressed by the general form as 10a+b, where a is the digit at the tens place and b is the digit at the unit’s place.
So, assume the digit at the units’ place of the original number is x. So, using the first condition, the digit at the tens place will be 3x. Then using the general from of a two-digit number, the original number will be,

10 (3 x) + x = 30 x + x = 31 x

Next, as per the second condition, the digits are reversed, so the digit at the unit’s place will become 3x and that at the tens place will be x. Thus, the new number so formed will be,