Question

The sum of a number and its reciprocal is $2\frac{1}{20}.$ The number is
(a) $\frac{5}{4}$
(b) $\frac{4}{3}$
(c) $\frac{3}{4}$
(d) $\frac{1}{6}$

Answer 1

(a) $\frac{5}{4}$

$$\begin{gathered} \text{Let the required number be}x. \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}: \\ x+\frac{1}{x}=\frac{41}{20} \\ \Rightarrow \frac{x^2+1}{x}=\frac{41}{20} \\ \Rightarrow 20x^2-41x+20=0 \\ \Rightarrow 20x^2-25x-16x+20=0 \\ \Rightarrow 5x(4x-5)-4(4x-5)=0 \\ \Rightarrow (4x-5)(5x-4)=0 \\ \Rightarrow x=\frac{5}{4}\text{or}x=\frac{4}{5} \end{gathered}$$