Q. 815.0( 1 Vote )

A two-dig

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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