Divide Rs. 1500 between A, B and C. So that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. Find C share.

Total amount = 1500

$\text{A}=\frac{1}{3}(\text{B}+\text{C})\Rightarrow 3\text{A}=\text{B}+\text{C}\Rightarrow 3\text{A}-\text{C}=\text{B}$

$\text{B}=\frac{2}{3}(\text{A}+\text{C}) 3\left(\frac{5\text{C}}{7}\right)=\text{B}+\text{C}$

$\text{3A}-\text{C}=\frac{2}{3}(\text{A}+\text{C})$                    $\frac{15\text{C}}{7}=\text{B}+\text{C}$

$\text{9A}-3\text{C}=2\text{A}+2\text{C}$                  $\frac{15\text{C}}{7}-\text{C}=\text{B}$

$7\text{A}=5\text{C}$                                        $\frac{8\text{C}}{7}=\text{B}$

$\text{A}=\frac{5\text{C}}{7}$

A + B + C = 1500

$\frac{5\text{C}}{7}+\frac{\text{8C}}{7}+\text{C}=1500$

$5\text{C}+\text{8C}+7\text{C}=1500\times 7$

$\text{C}=\frac{1500\times 7}{20}$

C = 525