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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?

A. 5 : 7 : 8 B. 20 : 49 : 64 C. 38 : 28 : 21 D. None of these Answer: Option B
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Solution(By Apex Team)

Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively. Then, 14x : 8y : 7z = 5 : 7 : 8. Now $\begin{aligned}&\frac{14x}{8y}=\frac{5}{7}\Rightarrow98x=40y\\ &\Rightarrow y=\frac{49x}{20}\\ &\text{ And, }\frac{14x}{7z}=\frac{5}{8}\\ &\Rightarrow112x=35z\\ &\Rightarrow z=\frac{112x}{35}=\frac{16x}{5}\\ &\text{ So }x:y:z=x:\frac{49x}{20}:\frac{16x}{5}\\ &\text{ (Multiply by 20) }\\ &\Rightarrow20:49:64\end{aligned}$

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