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

Asked by Topperlearning User 7th November 2013, 3:02 AM
Answered by Expert
Answer:
Let the ten's digit be x and unit's digit be y.

Number = 10x + y

xy=12 y = … (i)

Also, 10x+y+36 = 10y+x

9x-9y+36 = 0

x-y+4 = 0 … (ii)

From (i) and (ii),

x+4 =

x2+4x-12=0

(x+6)(x-2) =0

x=2 or x=-6

Rejecting x = -6, we have x = 2.

y= ==6

Thus, the required number is 2 x 10 + 6 = 26.

Answered by Expert 7th November 2013, 5:02 AM
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