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?

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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?

A20 : 64 : 49

B64 : 49 : 20

C20 : 49 : 64

D49 : 64 : 20

Answer:

B. 64 : 49 : 20

Read Explanation:

Solution: 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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