ABC26GN3011 · Ratio and Proportion
Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
If $\frac{a}{b}=\frac{4}{5}$ and $\frac{b}{c}=\frac{15}{16}$, then $\frac{c^{2}-a^{2}}{c^{2}+a^{2}}$ would be
(a)$\frac{1}{7}$
(b)$\frac{3}{4}$
(c)$\frac{7}{25}$
(d)None of these
Answer
Explanation
$$\begin{aligned} & \frac{a}{b}=\frac{4}{5} \text { and } \frac{b}{c}=\frac{15}{16} \Rightarrow \frac{a}{c}=\frac{a}{b} \times \frac{b}{c}=\frac{4}{5} \times \frac{15}{16}=\frac{3}{4} \Rightarrow \frac{c}{a}=\frac{4}{3} \\ & \Rightarrow \frac{c^{2}}{a^{2}}=\frac{16}{9} \Rightarrow \frac{c^{2}-a^{2}}{c^{2}+a^{2}}=\frac{\frac{c^{2}}{a^{2}}-1}{\frac{c^{2}}{a^{2}}+1}=\frac{\frac{16}{9}-1}{\frac{16}{9}+1}=\frac{7}{9} \times \frac{9}{25}=\frac{7}{25} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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