A) \[\frac{6P}{7}\]
B) \[\frac{9P}{7}\]
C) \[\frac{36P}{7}\]
D) \[6P\]
Correct Answer: B
Solution :
\[\begin{matrix} X \\ a \\ a-x \\ \end{matrix}\begin{matrix} \\ {} \\ {} \\ \end{matrix}\begin{matrix} Y \\ a \\ x \\ \end{matrix}\begin{matrix} + \\ {} \\ {} \\ \end{matrix}\begin{matrix} Z \\ a \\ x \\ \end{matrix}\] \[P_{x}^{'}=P\frac{(a-x)}{(a+x)}=\frac{P}{7}\] \[7a-7a=a+x\] \[6a=8x\] \[x=\frac{6a}{8}=\frac{3a}{4}\] \[{{K}_{P}}=\frac{{{x}^{2}}}{(a-x)}\frac{[P]}{\left[ a+x] \right]}\] \[=\frac{{{\left( \frac{3a}{4} \right)}^{2}}[P]}{\left( a-\frac{3a}{4} \right)\left( a+\frac{3a}{4} \right)}\] \[=\frac{9{{a}^{2}}\times 4\times 4\times P}{16\times a\times 7a}\] \[{{K}_{P}}=\frac{9P}{7}\]
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