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Three partners shared the profit in a business in the ratio 8 : 7 : 5. They invested their capitals for 7 months, 8 months and 14 months, respectively. What was the ratio of their capitals?
1. 20 : 64 : 49
2. 64 : 49 : 20
3. 20 : 49 : 64
4. 49 : 64 : 20

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Correct Answer - Option 2 : 64 : 49 : 20

Given:

Profit ratio of three partners = 8 : 7 : 5

Period of investment of 1st partner = 7 months

Period of investment of 2nd partner = 8 months

Period of investment of 3rd partner = 14 months

Concept used:

Person’s Profit = Investment × time period

Calculation:

Let the investment and time period be 7x : 8y : 14z

7x/8y = 8/7

⇒ 49x = 64y

⇒ y = 49x/64

7x/14z = 8/5

⇒ 35x = 112z

⇒ z = 35x/112

⇒ z = 5x/16

x : y : z = x : 49x/64 : 5x/16

⇒ Multiply by 64

x : y : z = 64 : 49 : 20

The investment ratio is 64 : 49 : 20

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