ABC26GN2930 · Ratio and Proportion

$A = \frac{2}{5}(B+C)$, $B = \frac{3}{7}(A+C)$. $\Rightarrow A = \frac{2}{5}\left(\frac{3}{7}A + \frac{3}{7}C + C\right) = \frac{6}{35}A + \frac{4}{7}C \Rightarrow \frac{29}{35}A = \frac{4}{7}C \Rightarrow A = \frac{4}{7} \times \frac{35}{29}C = \frac{20}{29}C$. $B = \frac{3}{7}\left(\frac{20}{29}C + C\right) = \frac{3}{7} \times \frac{49}{29}C = \frac{21}{29}C$. $\therefore A:B:C = \frac{20}{29}C:\frac{21}{29}C:C = 20:21:29$. Sum of ratio terms = (20+21+29) = 70. A's share = $₹\left(1050 \times \frac{20}{70}\right) = ₹300$; B's share = $₹\left(1050 \times \frac{21}{70}\right) = ₹315$; C's share = $₹\left(1050 \times \frac{29}{70}\right) = ₹435$.