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1. A, B and C enter into a partnership with capitals in the ratio 5 : 6 : 8. At the end of the business term, they received the profit in the ratio 5 : 3 : 12. Find the ratio of time for which they contributed their capitals ?

A. 2 : 1 : 3

B. 1 : 2 : 3

C. 2 : 3 : 1

D. 3 : 2 : 1

Solution:

\begin{aligned} Here p_{1} : p_{2} : p_{3} = 5 : 3 : 12 \\ and x_{1} : x_{2} : x_{3} = 5 : 6 : 8 \\ According to the formula \\ Required ratio \\ = \frac{p_{1}}{x_{1}} : \frac{p_{2}}{x_{2}} : \frac{p_{3}}{x_{3}} \\ = \frac{5}{5} : \frac{3}{6} : \frac{12}{8} \\ = 1 : \frac{1}{2} : \frac{3}{2} \\ = 2 : 1 : 3 \\ A l t e r n a t e : \\ Profit = Time \times Capital invested \\ Time = \frac{Profit}{Capital invested} \\ Required ratio of time \\ = \frac{5}{6} : \frac{3}{6} : \frac{12}{8} \\ = 1 : \frac{1}{2} : \frac{3}{2} \\ = 2 : 1 : 3 \end{aligned}

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