Question

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

Answer 1

here is your answer
if x=15 then y=27-x=27-15=12
if x=12 then y=27-x=27-12=15

Answer 2

Answer:

The required parts in which 27 is divided are 12 and 15

Step-by-step explanation:

Let the two parts in which 27 is divided be x and y

⇒ x + y = 27

⇒ x = 27 - y .......(1)

Also, sum of their reciprocals is given to be 3 by 20

$\implies \frac{1}{x}+\frac{1}{y}=\frac{3}{20}\\\\\text{Putting value of x from equation 1}\\\\\implies \frac{1}{27-y}+\frac{1}{y}=\frac{3}{20}\\\\\implies \frac{y+27-y}{y(27-y)}=\frac{3}{20}\\\\\implies 540=-3y^2+81y$

⇒ y² - 27y + 180 = 0

⇒ y = 12 or y = 15

If y = 12 then x = 15

If y = 15 then x = 12

Thus, The required parts in which 27 is divided are 12 and 15