Discussion
A, B and C did certain investments and the ratio of the durations of their investments is 3 : 2 : 7 respectively. Ratio of the profits of A, B and C is 4 : 3 : 14 respectively. What is the ratio of the investments of A, B and C ?
Answer: C
The investments are in the ratio 8 : 9 : 12.
Profit is proportional to investment times duration, so investment is proportional to profit divided by duration:
\[ \begin{aligned} \frac{4}{3} : \frac{3}{2} : \frac{14}{7} &= \frac{4}{3} : \frac{3}{2} : 2 \\ &= 8 : 9 : 12 \quad (\times 6) \end{aligned} \]
Check: \(8 \times 3 : 9 \times 2 : 12 \times 7 = 24 : 18 : 84 = 4 : 3 : 14\). Multiplying profit by duration instead of dividing gives a different, wrong ratio.
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