A) \[\frac{1}{7}\]
B) \[\frac{7}{25}\]
C) \[\frac{3}{4}\]
D) None of these
Correct Answer: B
Solution :
\[\frac{a}{c}=\left( \frac{a}{b}\times \frac{b}{c} \right)=\left( \frac{4}{5}\times \frac{15}{16} \right)=\frac{3}{4}\]\[\Rightarrow \]\[\frac{c}{a}=\frac{4}{3}\] \[\frac{({{c}^{2}}-{{a}^{2}})}{({{c}^{2}}+{{a}^{2}})}=\frac{\frac{{{c}^{2}}}{{{a}^{2}}}-1}{\frac{{{c}^{2}}}{{{a}^{2}}}+1}=\frac{{{\left( \frac{c}{a} \right)}^{2}}-1}{{{\left( \frac{c}{a} \right)}^{2}}+1}=\frac{\frac{16}{9}-1}{\frac{16}{9}+1}=\frac{(7/9)}{25/9}=\frac{7}{25}\]
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