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?

Answer: Option B

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,
$$\begin{array}{rl}& \frac{14x}{8y}=\frac{5}{7}\Rightarrow 98x=40y\\ & \Rightarrow y=\frac{49x}{20}\\ & \text{And, }\frac{14x}{7z}=\frac{5}{8}\\ & \Rightarrow 112x=35z\\ & \Rightarrow z=\frac{112x}{35}=\frac{16x}{5}\\ & \text{So}x:y:z=x:\frac{49x}{20}:\frac{16x}{5}\\ & (\text{Multiply by 20})\\ & \Rightarrow 20:49:64\end{array}$$