If p+1/q=1 and q+1/r=1, then the value of r+1/p is?

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{have} \\ \mathrm{p}+\frac{1}{\mathrm{q}}=1 \\ \Rightarrow \mathrm{p}=1-\frac{1}{\mathrm{q}} \\ \Rightarrow \mathrm{p}=\frac{\mathrm{q}-1}{\mathrm{q}} \\ \Rightarrow \frac{1}{\mathrm{p}}=\frac{\mathrm{q}}{\mathrm{q}-1} ......\left(1\right) \\ \mathrm{And}, \\ \mathrm{q}+\frac{1}{\mathrm{r}}=1 \\ \Rightarrow \frac{1}{\mathrm{r}}=1-\mathrm{q} \\ \Rightarrow \mathrm{r}=\frac{1}{1-\mathrm{q}} ......\left(2\right) \\ \mathrm{Adding} \mathrm{equation}\left(1\right) \mathrm{and} \left(2\right), \\ \frac{1}{\mathrm{p}}+\mathrm{r}=\frac{\mathrm{q}}{\mathrm{q}-1}+\frac{1}{1-\mathrm{q}} \\ =\frac{-\mathrm{q}+1}{1-\mathrm{q}} \\ =1 \\ \Rightarrow \frac{\mathbf{1}}{\mathbf{p}}\mathbf{+}\mathbf{r}\mathbf{=}\mathbf{1} \end{gathered}$$
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