Question

In a partnership, A invests $\frac{1}{6}$ of the capital for $\frac{1}{6}$ of the period. B invests $\frac{1}{3}$ of the capital for $\frac{1}{3}$ of the period and C, the rest of the capital for the entire period. What is A's share of the total profit of Rs. 2,300?

Accepted Answer

A. Let total capital = $C = 1$, total time = $T = 1$. - A's investment equivalent = $\frac{1}{6} 	imes \frac{1}{6} = \frac{1}{36}$. - B's investment equivalent = $\frac{1}{3} 	imes \frac{1}{3} = \frac{1}{9} = \frac{4}{36}$. - C's capital = $1 - \left(\frac{1}{6} + \frac{1}{3}ight) = 1 - \frac{1}{2} = \frac{1}{2}$. C's investment equivalent = $\frac{1}{2} 	imes 1 = \frac{1}{2} = \frac{18}{36}$. Ratio of profit shares $A : B : C = 1 : 4 : 18$. Sum of terms = $1 + 4 + 18 = 23$. A's share = $\frac{1}{23} 	imes 2300 = 	ext{Rs. } 100$.

Partnership Profit Share

Explanation

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