Answer :

Let the units digit be x.

Then the ten's digit is .

Therefore the required number is

The new number after interchanging their places is

.

Condition: When 36 is added to this number, the digits interchange their places.

120 + x ^{ 2 } + 36x = 10x ^{ 2 } + 12

9x ^{ 2 } - 36x – 108 = 0

x ^{ 2 } - 4x – 12 = 0

x ^{ 2 } - 6x + 2x – 12 = 0

x(x – 6) + 2(x – 6) = 0

(x + 2)(x – 6) = 0

(x + 2) = 0 or (x – 6) = 0

x = -2 or x = 6

Therefore the required number is

Checking:

Old number = 26.

New number = 62.

New number = 26 + 36 = 62.

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