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1. 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

Solution:

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

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