3 brothers divided 1620 among them in such a way that the share of second is equal to $$\frac{5}{{13}}$$ of share of other two, combined. What is the share of the second one ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Given share of }}{{\text{2}}^{{\text{nd}}}} \cr & = \frac{5}{{13}}{\text{of}}\left( {{{\text{1}}^{{\text{st}}}} + {{\text{3}}^{{\text{rd}}}}} \right) \cr & {\text{or, }}\frac{{{{\text{2}}^{{\text{nd}}}}}}{{{{\text{1}}^{{\text{st}}}}{\text{ + }}{{\text{3}}^{{\text{rd}}}}}} = \frac{5}{{13}} \cr & \therefore {1^{{\text{st}}}} + {{\text{2}}^{{\text{nd}}}} + {{\text{3}}^{{\text{rd}}}} = 13 + 5 = 18 \cr & \because 18{\text{units}} = 1620 \cr & \therefore {\text{1 unit}} = \frac{{1620}}{{18}} \cr & \therefore 5{\text{ units}} = \frac{{1620}}{{18}} \times {\text{5}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4{\text{50}} \cr & {\text{Hence share of }}{{\text{2}}^{{\text{nd}}}} = {\text{Rs}}{\text{.}}\,{\text{450}} \cr} $$