A sum of ₹ 12540 is divided among A, B and C so that A may receive 3/7 of what B and C together receive and B… · ABC26GN3089

$A=\frac{3}{7}(B+C) ; B=\frac{2}{9}(A+C)$. $\Rightarrow A=\frac{3}{7}\left(\frac{2}{9} A+\frac{2}{9} C+C\right)=\frac{3}{7}\left(\frac{2}{9} A+\frac{11}{9} C\right)=\frac{2}{21} A+\frac{11}{21} C$. $\Rightarrow \frac{19 A}{21}=\frac{11}{21} C \Rightarrow A=\left(\frac{21}{19} \times \frac{11}{21}\right) C=\frac{11}{19} C$. $\therefore B=\frac{2}{9}\left(\frac{11}{19} C+C\right)=\left(\frac{2}{9} \times \frac{30}{19}\right) C=\frac{20}{57} C$. So, $A: B: C=\frac{11}{19} C: \frac{20}{57} C: C=33: 20: 57$. Sum of ratio terms $=(33+20+57)=110$. A's share $=₹\left(12540 \times \frac{33}{110}\right)=₹ 3762$. $\therefore$ Required difference $=₹(3762-2280)=₹ 1482$.