If a + b = 1, c + d = 1 and a - b = d/c , then the value of c2 - d2 = ?

Answer: Option B

\begin{aligned} & a + b = 1 \\ & c + d = 1 \\ & a - b = \frac{d}{c} \\ & or\,\,\frac{1}{{a - b}} = \frac{c}{d} \\ & \Rightarrow \frac{{a + b}}{{a - b}} = \frac{c}{d}\left( {\therefore a + b = 1} \right) \\ & {\text{By C & D rule }} \\ & \Rightarrow \frac{{\left( {a + b} \right) + \left( {a - b} \right)}}{{\left( {a + b} \right) - \left( {a - b} \right)}} = \frac{{c + d}}{{c - d}} \\ & \Rightarrow \frac{{2a}}{{2b}} = \frac{{c + d}}{{c - d}} \\ & \Rightarrow \frac{a}{b} = \frac{{c + d}}{{c - d}} \\\end{aligned}
Now multiply & divide by (c + d)
$$\begin{array}{rl}& \frac{a}{b}=\frac{\left(c+d\right)}{\left(c-d\right)}\times \frac{\left(c+d\right)}{\left(c+d\right)}=\frac{{\left(c+d\right)}^2}{c^2-d^2}\\ & \Rightarrow \frac{a}{b}=\frac{{\left(c+d\right)}^2}{\left(c^2-d^2\right)}\\ & \Rightarrow c+d=1\\ & \Rightarrow \frac{a}{b}=\frac{1}{c^2-d^2}\\ & \Rightarrow c^2-d^2=\frac{b}{a}\end{array}$$