question_answer

In the given figure, \[PA=5\text{ }cm,\text{ }RC=3\text{ }cm,\]then find the value of QB.

A)  \[7\,cm\]                      

B)  \[7.5\,cm\]

C)  \[8\,cm\]                      

D)  \[4\,cm\]

Correct Answer: B

Solution :

       Apply, \[\frac{1}{PA}+\frac{1}{QB}=\frac{1}{RC}\] \[\Rightarrow \,\,\,\,\frac{1}{5}+\frac{1}{QB}=\frac{1}{3}\Rightarrow \frac{1}{5}-\frac{1}{3}=-\frac{1}{QB}\] \[\Rightarrow \,\,\,\,-\frac{2}{15}=-\frac{1}{QB}=\,\Rightarrow QB=\frac{15}{2}\] \[QB=\underline{\mathbf{7}\mathbf{.5}\,\mathbf{cm}}\]