Question : A, B, and C made certain investments and the ratio of their time periods is 3 : 2 : 7 respectively. The 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?
Option 1: 1 : 3 : 4
Option 2: 7 : 9 : 11
Option 3: 8 : 9 : 12
Option 4: 2 : 3 : 11
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Correct Answer: 8 : 9 : 12
Solution :
We know that, profit = investment × time
So, investment = $\frac{\text{Profit}}{\text{Time}}$
Now, the ratio of their profit = 4 : 3 : 14
and the ratio of their time periods = 3 : 2 : 7
Therefore, the ratio of their investment = $\frac{4}{3}:\frac{3}{2}:\frac{14}{7}$ = 8 : 9 : 12
Hence, the correct answer is 8 : 9 : 12.
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