Question

divide 27 into two parts such that the sum of their reciprocals is 3/20​

Answer 1

check the Attachment

Answer 2

let the two parts be X and Y then X+Y=27
let , X= 27-Y...........eq 1
according to the question ,
1/x+1/y = 3/20
applying x value Frome equation 1
then , 1/ 27-y + 1/y= 3/20
y+27-y/27y-y² = 3/20
27/ 27y-y² =3/20
cross multiplication ,,
540 = 81y- 3y²
therefore 3y²-81y+540=0
dividing by 3

y²-27y+180=0
therefore y=. 15 or. 12
therefore X= 27 - 15= 12 or 27- 12= 15
therefore the two parts of 27 is 15 and 12