a) 100 m
b) $$111\frac{1}{9}$$ m
c) 25 m
d) 50 m

Answer: a
Explanation:
$$\eqalign{ & {\text{When}}\,{\text{B}}\,\,{\text{runs}}\,{\text{25m,}}\,{\text{A}}\,{\text{runs}}\,\frac{{45}}{2}m \cr & {\text{When}}\,{\text{B}}\,\,{\text{runs}}\,{\text{1000m,}}\,{\text{A}}\,{\text{runs}} \cr & = \left( {\frac{{45}}{2} \times \frac{1}{{25}} \times 1000} \right)m \cr & = 900 \,m \cr & {\text{B}}\,{\text{beats}}\,{\text{A}}\,{\text{by}}\,{\text{100 m}} \cr} $$