Three partners shared the profit in a busines | vedclass

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(D) Let the investments of the three partners be $I_1, I_2,$ and $I_3$ respectively.Profit is distributed in the ratio of (Investment $	imes$ Time).G

Vedclass · Accepted Answer

$20: 49: 64$

Vedclass · Answer

(D) Let the investments of the three partners be $I_1, I_2,$ and $I_3$ respectively.Profit is distributed in the ratio of (Investment $	imes$ Time).Given ratio of profit = $5: 7: 8$.Time periods are $T_1 = 14$ months,$T_2 = 8$ months,and $T_3 = 7$ months.So,$(I_1 	imes 14) : (I_2 	imes 8) : (I_3 	imes 7) = 5 : 7 : 8$.From this,we have:$I_1 = \frac{5}{14}, I_2 = \frac{7}{8}, I_3 = \frac{8}{7}$ (in terms of profit units per month).To find the ratio $I_1 : I_2 : I_3$,we calculate $\frac{5}{14} : \frac{7}{8} : \frac{8}{7}$.Multiply by the $LCM$ of denominators $(14, 8, 7)$,which is $56$.$I_1 : I_2 : I_3 = (\frac{5}{14} 	imes 56) : (\frac{7}{8} 	imes 56) : (\frac{8}{7} 	imes 56)$.$I_1 : I_2 : I_3 = (5 	imes 4) : (7 	imes 7) : (8 	imes 8)$.$I_1 : I_2 : I_3 = 20 : 49 : 64$.

Three partners shared the profit in a business in the ratio $5: 7: 8$. They had partnered for $14$ months,$8$ months,and $7$ months respectively. What was the ratio of their investments?

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