Discussion
X ,Y and Z enter into a partnership by investing their capitals in the ratio 8 : 5 : 4. At the end of a year, the profit was distributed among X, Y and Z in the ratio 6 : 3 : 2. What is the ratio of time for which X,Y and Z invested their capitals?
Answer: B
The ratio of the times is 15 : 12 : 10. Profit is proportional to the capital multiplied by the time, so the time is proportional to profit divided by capital.
\[ t_X : t_Y : t_Z = \frac{6}{8} : \frac{3}{5} : \frac{2}{4} \]
\[ = 0.75 : 0.6 : 0.5 = 15 : 12 : 10 \]
The options 13 : 8 : 5, 18 : 5 : 9 and 20 : 15 : 8 do not match these three values, so the second option is the answer. As a check, capitals of 8, 5 and 4 units for times of 15, 12 and 10 give products of 120, 60 and 40, which are in the ratio 6 : 3 : 2 of the profits.
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