Divide Rs. 671 among A, B and C such that if their shares be increased by Rs. 3, Rs. 7 and Rs. 9 respectively the remainder shall be in the ratio 1 : 2 : 3.

$$\eqalign{ & {\text{Remainder}} \cr & = {\text{Rs}}{\text{.}}\left[ {671 + \left( {3 + 7 + 9} \right)} \right] \cr & = {\text{Rs}}{\text{. }}690 \cr & {\text{A's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {\left( {690 \times \frac{1}{6}} \right) - 3} \right] \cr & = {\text{Rs}}{\text{. }}112 \cr & {\text{B's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {\left( {690 \times \frac{2}{6}} \right) - 7} \right] \cr & = {\text{Rs}}{\text{. }}223 \cr & {\text{C's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {\left( {690 \times \frac{3}{6}} \right) - 9} \right] \cr & = {\text{Rs}}{\text{. }}336 \cr} $$