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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 ?

A. Rs. 1170 B. Rs. 450 C. Rs. 540 D. Rs. 500 Answer: Option B
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Solution(By Apex Team)

$\begin{array}{l}\text{Given share of }2^{\text{nd}}\\ =\frac{5}{13}\mathrm{of}\left(1^{\mathrm{st}}+3^{\mathrm{rd}}\right)\\ \text{ or, }\frac{2^{\text{nd }}}{1^{\text{st }}+3^{\text{rd }}}=\frac{5}{13}\\ \therefore1^{\text{st }}+2^{\text{nd }}+3^{\text{rd }}=13+5=18\\ \because\text{ 18units }=1620\\ \therefore1\text{ unit }=\frac{1620}{18}\\ \therefore5\text{ units }=\frac{1620}{18}\times5\\ =450\\ \text{Hence share of 2}^{\text{nd}}\ =\ \text{Rs.}\ 450\end{array}$

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