If \[\frac{a}{b}=\frac{4}{5}\]and \[\frac{b}{c}=\frac{15}{16},\]then\[\frac{{{c}^{2}}+{{a}^{2}}}{{{c}^{2}}+{{a}^{2}}}\]is equal to _______.

• A. \[\frac{1}{7}\]                          
• B. \[\frac{7}{25}\] 
• C. \[\frac{3}{4}\]              
• D.        \[\frac{7}{15}\]