Question

The number 50 is divided into two parts such that the sum of their reciprocals is $\frac{1}{12}$ then these parts are

• A. 30 and 20
• B. 10 and 40
• C. 25 and 25
• D. 15 and 35

Answer 1

Answer: (A)

30 and 20

Let the two parts be x and 50-x
then, according to the question
$\frac{1}{x}+\frac{1}{50-x}=\frac{1}{12}$

$\Rightarrow \frac{50}{x(50-x)}=\frac{1}{12}$

$\Rightarrow x(50-x)=600$

$\Rightarrow x^2-50x+600=0$

$\Rightarrow (x-20)(x-30)=0$

$\Rightarrow$ x=20 or 30