a) Rs. 2000, 3.5 years and 4 years
b) Rs. 1500, 3.5 years and 4 years
c) Rs. 2000, 4 years and 5.5 years
d) Rs. 3000, 4 years and 4.5 years

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