Question

Divide 40 into two parts such that sum of their reciprocal be 8/75​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The numbers would be 15 or 25

Step-by-step explanation:

Given the sum of the reciprocal of two numbers whose sum is $40$, is  $\frac{8}{75}$.

Let us assume that the first number is $x$.

Then the second number would be $40-x$.

Then, according to the question

$\frac{1}{x}+\frac{1}{40-x}=\frac{8}{75}$

Simplifying we get,

$\frac{40-x+x}{x(40-x)} =\frac{8}{75}\\ \\\frac{40}{x(40-x)}=\frac{8}{75}$

$40\times 75=8\times x(40-x)\\3000=8\times (40x-x^2)\\\frac{3000}{8}= (40x-x^2)\\375=(40x-x^2)\\x^2-40x+375=0$

Now, we need to solve this quadratic equation.

$x^2-25x-15x+375=0\\x(x-25)-15(x-25)=0\\(x-15)(x-25)=0\\x=15\ or \ x=25$

So, the numbers would be 15 or 25.