a two digit number is such that the product of its digits is 20.if 9 is added to the nber the number,the digits interchange their places.find the number
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x*y = 20
10x+y +9 = 10y + x
9y-9x = 9
y-x = 1
from eqn 1 we get x = 20/y
putting in
y-20/y = 1
y^2-20 = y
y^2-y -20 = 0
y^2-5y+4y -20 = 0
y(y-5) +4(y-5) = 0
(y -5)(y+4) = 0
So y = 5 or -4
taking positive value y = 5
then x = 4
So original no is 45.
10x+y +9 = 10y + x
9y-9x = 9
y-x = 1
from eqn 1 we get x = 20/y
putting in
y-20/y = 1
y^2-20 = y
y^2-y -20 = 0
y^2-5y+4y -20 = 0
y(y-5) +4(y-5) = 0
(y -5)(y+4) = 0
So y = 5 or -4
taking positive value y = 5
then x = 4
So original no is 45.
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