In a partnership firm, A invests \\(\\frac{1}{6}\\)th of the total investment for \\(\\frac{1}{6}\\)th of the tenure. B invests \\(\\frac{1}{3}\\)rd of the total investment for \\(\\frac{1}{3}\\)rd of the tenure while C invests the remaining part for the full duration. Out of total profit of \u20b946,00,000, what shall be C’s share ?<\/p>\n
[amp_mcq option1=”\u20b930,00,000″ option2=”\u20b932,00,000″ option3=”\u20b934,00,000″ option4=”\u20b936,00,000″ correct=”option4″]<\/p>\n
B’s investment $I_B = \\frac{1}{3} I$. B’s tenure $T_B = \\frac{1}{3} T$.
\nB’s profit share is proportional to $I_B \\times T_B = (\\frac{1}{3} I) \\times (\\frac{1}{3} T) = \\frac{1}{9} IT$.<\/p>\n
C invests the remaining part of the investment for the full duration.
\nC’s investment $I_C = \\text{Total Investment} – I_A – I_B$.
\n$I_C = I – \\frac{1}{6} I – \\frac{1}{3} I = I – (\\frac{1}{6} + \\frac{2}{6}) I = I – \\frac{3}{6} I = I – \\frac{1}{2} I = \\frac{1}{2} I$.
\nC’s tenure $T_C = T$ (full duration).
\nC’s profit share is proportional to $I_C \\times T_C = (\\frac{1}{2} I) \\times T = \\frac{1}{2} IT$.<\/p>\n
The ratio of the profit shares of A, B, and C is the ratio of their (Investment $\\times$ Time) products:
\nRatio = $\\frac{1}{36} IT : \\frac{1}{9} IT : \\frac{1}{2} IT$.
\nDividing by $IT$ (assuming $I, T > 0$):
\nRatio = $\\frac{1}{36} : \\frac{1}{9} : \\frac{1}{2}$.
\nTo simplify this ratio, multiply by the Least Common Multiple (LCM) of the denominators (36, 9, 2), which is 36.
\nRatio = $36 \\times \\frac{1}{36} : 36 \\times \\frac{1}{9} : 36 \\times \\frac{1}{2}$
\nRatio = $1 : 4 : 18$.<\/p>\n