Rs. 600 are divided among A, B, C so that Rs. 40 more than $$\frac{{\text{2}}}{{\text{5}}}$$ of A's share, Rs. 20 more than $$\frac{{\text{2}}}{{\text{7}}}$$ of B's share and Rs. 10 more than $$\frac{{\text{9}}}{{{\text{17}}}}$$ of C's share may all be equal. What is A's share ?

$$\eqalign{ & = \frac{2}{5}{\text{A}} + 40 = \frac{2}{7}{\text{B}} + 20 \cr & \Rightarrow \frac{2}{7}{\text{B}} = \frac{2}{5}{\text{A}} + 20 \cr & \Rightarrow {\text{B}} = \frac{7}{2}\left( {\frac{2}{5}{\text{A}} + 20} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{7}{5}{\text{A}} + 70} \right) \cr & {\text{And,}} \cr & = \frac{2}{5}{\text{A}} + 40 = \frac{9}{{17}}{\text{C}} + 10 \cr & \Rightarrow \frac{9}{{17}}{\text{C}} = \frac{2}{5}{\text{A}} + 30 \cr & \Rightarrow {\text{C}} = \frac{{17}}{9}\left( {\frac{2}{5}{\text{A}} + 30} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{34}}{{45}}{\text{A}} + \frac{{170}}{3} \cr & = {\text{A}} + {\text{B}} + {\text{C}} = 600 \cr & \Rightarrow {\text{A}} + \left( {\frac{7}{5}{\text{A}} + 70} \right) + \left( {\frac{{34}}{{45}}{\text{A}} + \frac{{170}}{3}} \right) = 600 \cr & \Rightarrow \frac{{142{\text{A}}}}{{45}} = 600 - \frac{{380}}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{1420}}{3} \cr & \Rightarrow {\text{A}} = \frac{{1420}}{3} \times \frac{{45}}{{142}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 150 \cr} $$