• # question_answer The sum of two numbers is 8 and the sum 8 of their reciprocals is$\frac{8}{15}$. Find the numbers. A)  5, 3                             B)  7, 1     C)         4, 4     D)                     2, 6

Let the two numbers be x and y. According to the given conditions, $x+y=8~$                                        ....(1) and   $\frac{1}{x}+\frac{1}{y}=\frac{8}{15}$                              ....(2) Putting value of $x=8-y$in (2), we get $\frac{1}{8-y}+\frac{1}{y}=\frac{8}{15}$   $\Rightarrow$  $\frac{y+8-y}{y(8-y)}=\frac{8}{15}$ $\Rightarrow$${{y}^{2}}-8y+15=0$$\Rightarrow$ ${{y}^{2}}-5y-3y+15=0$ $\Rightarrow$$(y-5)\,(y-3)=0$ $\Rightarrow$$y=5$ or $y=3$ From (1), $x=3$or $x=5$ Thus, the numbers are 5 and 3.