question_answer

In the given figure, \[AB||PQ||CD,\]\[AB=x\] units, \[CD=y\] units and \[PQ=z\] units, then \[\frac{1}{x}+\frac{1}{y}=\]

A)  \[2/z\]             

B)  \[1/z\] 

C)  \[{{z}^{2}}\]                      

D)         z

Correct Answer: B

Solution :

Let BQ = a units and QD = b units. Now, using BPT in \[\Delta DBA,\]we have             \[\frac{b}{a+b}=\frac{z}{x}\]                                  ?.(i) Again, using BPT in \[\Delta BDC,\]we have   \[\frac{a}{a+b}=\frac{z}{y}\]                                  ?.(ii) Adding (i) and (ii), we get        \[\frac{a+b}{a+b}=\frac{z}{x}+\frac{z}{y}\Rightarrow 1=z\left( \frac{1}{x}+\frac{1}{y} \right)\Rightarrow \frac{1}{x}+\frac{1}{y}=\frac{1}{z}\]