The investments of three people in a business are in the ratio of 2:3:5 and their profit at the end of two years are in the ratio of 1:2:3. Find the ratio of the periods of their investments?
Question
The investments of three people in a business are in the ratio of 2:3:5 and their profit at the end of two years are in the ratio of 1:2:3. Find the ratio of the periods of their investments?
Solution
The ratio of their investments is 2:3:5 and the ratio of their profits is 1:2:3.
The profit made by an investor is directly proportional to the product of the investment and the time period for which the investment is made. Therefore, if P1, P2, and P3 are the profits made by the three investors, I1, I2, and I3 are their respective investments, and T1, T2, and T3 are the respective time periods for which the investments are made, we have:
P1/P2 = (I1T1) / (I2T2) and P2/P3 = (I2T2) / (I3T3)
Substituting the given ratios, we get:
1/2 = (2T1) / (3T2) and 2/3 = (3T2) / (5T3)
Solving these equations, we get:
T1/T2 = 3/4 and T2/T3 = 4/5
Therefore, the ratio of the periods of their investments is 3:4:5.
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