Question

Divide 27 into two parts such that the sum of their reciprocals is 3/20.

Answer 1

make a quadratic equation where first part is x and second part is (27-x)

1/x+ 1/(27-x)= 3/20
solve it
x= 15;x= 12

Answer 2

Answer:

The two parts in which 27 must be divided are : 12 and 15

Step-by-step explanation:

Let first number be x and second number be y

Now, x + y = 27

⇒ x = 27 - y ........(1)

$\text{Sum of their reciprocals is }\frac{3}{20}\\\\\implies \frac{1}{x}+\frac{1}{y}=\frac{3}{20}.........(2)\\\\\text{Substituting value ox from equation 1 into equation 2}\\\\\implies \frac{1}{27-y}+\frac{1}{y}=\frac{3}{20}\\\\\implies y^2-27y+180=0\\\\\implies y = 12\text{ and }15\\\\\text{Now, putting these values of x in equation (1)}\\\\\implies x=12\text{ and }27$

Hence, the two parts in which 27 must be divided are : 12 and 15