Rs. 2010 are to be divided among A, B, C in such a way that if A gets Rs. 5, then B must get Rs. 12 and if B gets Rs. 4, then C must get Rs. 5.50. The share of C will exceed that of B by -

Explanation:-

$$\eqalign{ & {\text{A}}:{\text{B}} = 5:12 \cr & {\text{B}}:{\text{C}} = 4:5.50 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 12:16.5 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 12:\frac{{33}}{2}. \cr & {\text{A}}:{\text{B}}:{\text{C}} = 5:12:\frac{{33}}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10:24:33. \cr & {\text{Sum of ratio terms}} \cr & = 10 + 24 + 33 \cr & = 67. \cr & {\text{C's share}} = {\text{Rs}}{\text{.}}\left( {2010 \times \frac{{33}}{{67}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}990. \cr & B'{\text{s share}} = {\text{Rs}}{\text{.}}\left( {2010 \times \frac{{24}}{{67}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.720. \cr & {\text{Required difference}} \cr & = {\text{Rs}}{\text{.}}\left( {990 - 720} \right) \cr & = {\text{Rs}}{\text{. }}270. \cr}$$