The ratio of weights of two spheres of different materials is 8 : 17 and the ratio of weights per 1 cc of materials of each is 289 : 64. The ratio of radii of the two spheres is

Solution (By Examveda Team)

Ratio of volume of sphere × ratio of weight per 1 cc of material of each = Ratio of weight of two sphere
$$\eqalign{ & \frac{{\frac{4}{3}\pi r_1^3}}{{\frac{4}{3}\pi r_2^3}} \times \frac{{289}}{{64}} = \frac{8}{{17}} \cr & \frac{{r_1^3}}{{r_2^3}} = \frac{{8 \times 64}}{{17 \times 289}} \cr & \frac{{{r_1}}}{{{r_2}}} = \frac{{8 \times 8 \times 8}}{{17 \times 17 \times 17}} \cr & \frac{{{r_1}}}{{{r_2}}} = \frac{8}{{17}} \cr & {r_1}:{r_2} = 8:17 \cr} $$