Sum of two number is 50 & sum of three reciprocal is 1/12 so find these two numbers

Sol : x+y = 50 .....(1) x=50-y ....(2)
1x+1y=1121x+1y=112 ⇒y+xxy=112⇒12(y+x)=xy⇒y+xxy=112⇒12(y+x)=xy ...(3)
put (2) in (4)
⇒⇒ 12(y+50-y)=(50-y)y
⇒⇒ 12y+600-12y=50y-y2y2
⇒⇒ y2y2-50y+600=0
⇒⇒ y2y2-30y-20y+600=0
⇒⇒ y(y-30)-20(y-30)=0
⇒⇒ (y-20) (y-30)=0
y=20 or y=30
if y=20 then x = 30
or y=30 then x = 20
two numbers are 30 & 20
Answer:E