A two-digit number is such that the product of its digits is 12. When 36is added to this number, the digits interchange their places. Find thenumber.
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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