Answer: Option A
$$\eqalign{
& {\text{Let each sum}} = {\text{Rs}}{\text{. }}x. \cr
& {\text{Let the first sum be invested for}} \cr
& \left( {T - \frac{1}{2}} \right){\text{years and}} \cr
& {\text{the second sum for }}T{\text{ years}}{\text{.}} \cr
& {\text{Then,}} \cr
& x + \frac{{x \times 8 \times \left( {T - \frac{1}{2}} \right)}}{{100}} = 2560 \cr
& \Rightarrow 100x + 8xT - 4x = 256000 \cr
& \Rightarrow 96x + 8xT = 256000....(i) \cr
& {\text{And,}} \cr
& x + \frac{{x \times 7 \times T}}{{100}} = 2560 \cr
& \Rightarrow 100x + 7xT = 256000....(ii) \cr
& {\text{From(i) and (ii), we get:}} \cr
& 96x + 8xT = 100x + 7xT \cr
& \Rightarrow 4x = xT \cr
& \Rightarrow T = 4 \cr
& {\text{Putting }}T = {\text{4 in (i),we get:}} \cr
& 96x + 32x = 256000 \cr
& \Rightarrow 128x = 256000 \cr
& \Rightarrow x = 2000 \cr
& {\text{Hence,}} \cr
& {\text{each sum}} = {\text{Rs}}{\text{. 2000}} \cr
& {\text{time periods}} = \cr
& {\text{4 years and }}3\frac{1}{2}{\text{years}} \cr} $$