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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?

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? Correct Answer 20 : 49 : 64

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

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