Question

Divide $27$ into two parts such that the sum of their reciprocals is $\frac{3}{20}$

Answer 1

Let two parts be $x$ and $y$

So, $x+y=\mathrm{27..........}\left(1\right)$

According to the question,

$\frac{1}{x}+\frac{1}{y}=\frac{3}{20}$

$\frac{x+y}{xy}=\frac{3}{20}$

$\frac{27}{xy}=\frac{3}{20}$

$y=\frac{180}{x}$

Putting this value in (1) we get

$x^2-27+180=0$

$x^2-15x-12x+180=0$

$x(x-15)-12(x-15)=0$

$(x-12)(x-15)=0$

$x=12$ or $x=15$

So the two parts of 27 are 12 and 15.