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$A$ and $B$ started a business together and the respective ratio between the investments of $A$ and $B$ was $5:9$. After $4$ months from the start of business, $C$ joined the business and the respective ratio between investments of $B$ and $C$ was $3:7$. If the annual profit earned by them was $\$ 7084$, what is $C$'s share in the profit?

My solution:

Ratio of investments of $A,B,C = 5:9:21$

Ratio of profits $= (5*12):(9*12):(21*8)=5:9:14$

Therefore $C$'s share$= (14/28)*7084=3542$

Is this the correct answer? In textbook, the correct answer is given as $\$ 3527$. Which one is correct?

Soumee
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1 Answers1

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I agree with you entirely.

For the first 4 months the ratio of investments is $5:9:0$

For the next 8 months the ratio is $5:9:21$

Weighted ratio is thus $(4 \times 5 + 8 \times 5):(4 \times 9 + 8 \times 9):(4 \times 0 + 8 \times 21)$

$60:108:168$

So C's share is $\frac {168}{336}\times £7084=\frac {1}{2}\times £7084=£3542$

I wonder if there is a mistake in the question. If the amount to share is in fact £7054, then C's share would be £3527.

tomi
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