Question

50 is divided  into two parts such that the sum of their reciprocal is 1/12.find the two parts .

Answer 1

50 is divided  into two parts.
lets say first number is x and second number is (50-x)

so, 50 + 1/(50-x) = 1/12

50 is divided  into two parts.
lets say first number is x and second number is (50-x)

so, 50 + 1/(50-x) = 1/12
(50-x+x)/x(50-x) = 1/12
=50/50x-x^2 = 1/12
Now do the cross multiplication
=50x-x^2=600
=x^2-50x+600=0
=(x-30)(x-20) = 0
so, x= 30 or 20

The two parts are  30 and (50-x) = 20. 

Answer 2

Let 50 be divided into two parts such that one of the part be x and the other part thus be (50-x). Hence 50=50-x+x.
As per the given question,
(1/(50-x))+(1/x)=1/12.
On solving this we get the two parts as 20 and 30.