The sum and products of two numbers are 12 and 35 respectively. The sum of ir reciprocals will be:

$$\eqalign{ & {\text{Let}}\,{\text{two}}\,{\text{numbers}}\,{\text{are}}\,x\,{\text{and}}\,y. \cr & {\text{Now,}}\,{\text{Sum}}\,{\text{of}}\,{\text{the}}\,{\text{numbers}}, \cr & x + y = 12 \cr & {\text{Product}}\,{\text{of}}\,{\text{the}}\,{\text{number}}, \cr & xy = 35 \cr & {\text{Then}}\,{\text{sum}}\,{\text{of}}\,{\text{the}}\,{\text{reciprocals}} \cr & = {\frac{1}{x}} + {\frac{1}{y}} \, \cr & = \frac{{ {x + y} }}{{xy}} \cr & = \frac{{12}}{{35}} \cr} $$