ABC26GN0969 · Simplification
Subject: General Aptitude · Chapter: Simplification · Exam: 2007 · Marks: · Difficulty:
If $\frac{a}{b}=\frac{4}{5}$ and $\frac{b}{c}=\frac{15}{16}$, then $\frac{c^{2}-a^{2}}{c^{2}+a^{2}}$ is
(a)$\frac{1}{7}$
(b)$\frac{7}{25}$
(c)$\frac{3}{4}$
(d)None of these
Answer
Explanation
$$\begin{aligned} & \frac{a}{b}=\frac{4}{5} \text { and } \frac{b}{c}=\frac{15}{16} \Rightarrow\left(\frac{a}{b} \times \frac{b}{c}\right)=\left(\frac{4}{5} \times \frac{15}{16}\right) \Rightarrow \frac{a}{c}=\frac{3}{4} . \\ & \therefore \frac{c^{2}-a^{2}}{c^{2}+a^{2}}=\frac{1-\left(\frac{a^{2}}{c^{2}}\right)}{1+\left(\frac{a^{2}}{c^{2}}\right)}=\frac{1-\left(\frac{a}{c}\right)^{2}}{1+\left(\frac{a}{c}\right)^{2}}=\frac{1-\frac{9}{16}}{1+\frac{9}{16}}=\frac{(7 / 16)}{(25 / 16)}=\frac{7}{25} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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