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(C) Let the investments of $A$ and $B$ be $3x$ and $8x$ respectively.$C$ invested $\frac{3}{4}$ of $B$'s investment,so $C$'s investment $= \frac{3}{4}

Vedclass · Accepted Answer

$90000$

Vedclass · Answer

(C) Let the investments of $A$ and $B$ be $3x$ and $8x$ respectively.$C$ invested $\frac{3}{4}$ of $B$'s investment,so $C$'s investment $= \frac{3}{4} 	imes 8x = 6x$.$A$ and $B$ invested for $12$ months,while $C$ invested for $(12 - 4) = 8$ months.The ratio of their profit shares is the ratio of (investment $	imes$ time):$A:B:C = (3x 	imes 12) : (8x 	imes 12) : (6x 	imes 8)$$= 36x : 96x : 48x$Dividing by $12x$,we get the ratio $3 : 8 : 4$.Let the total profit be $P$. $C$'s share is $\frac{4}{3+8+4} 	imes P = \frac{4}{15} 	imes P$.Given $C$'s share $= ₹ 24000$,so $\frac{4}{15} 	imes P = 24000$.$P = 24000 	imes \frac{15}{4} = 6000 	imes 15 = ₹ 90000$.

$A$ and $B$ started a partnership business by investing in the ratio of $3:8$. $C$ joined them after $4$ months with an amount equal to $\frac{3}{4}$ of $B$'s investment. What was the total profit (in ₹) at the end of the year if $C$ received ₹ $24000$ as his share?

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