The product of digits of a two digit number is 12. when 9 is added to the number, the digits interchange their places. Determine the number.
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let the no be (10x + y)
xy = 12 ⇒ y= 12/x
10x + Y +9 =10y +x
⇒9x +9 =9y
⇒x+1 = y
=12/x
⇒x² + x - 12 = 0
⇒x² +3x -4x - 12 = 0
⇒(x+3)(x-4) = 0 ∴ x = 4 [∵ digit cann't be -ve]
∴ y = 5
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