Question

divide 27 into two parts such that the sum of their reciprocal is 3 upon 20

Answer 1

$x + y = 27 \\ \frac{1}{x} + \frac{1}{y} = \frac{3}{20}$
solving this we get
$xy = 180$
by subsitution
$x(27 - x) = 180 \\ {x}^{2} - 27x + 180 = 0 \\ (x - 12)(x - 15) \\ x = 12$
or x=15
y=15 or 12