Question
Download Solution PDFThree partners shared the profit in a business in the proportion of 9 ∶ 8 ∶ 11. They invested their capitals for 4 months, 6 months and 18 months, respectively. What was the ratio of their capitals?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Three partners shared the profit in a business in the proportion of 9 ∶ 8 ∶ 11. They invested their capital for 4 months, 6 months, and 18 months, respectively.
Concept used:
Profit is shared according to the capital invested.
Total investment = Invested Capital × Time period of the investment
Calculation:
Let the invested capital by them be P, Q, and R respectively.
According to the concept,
(P × 4) : (Q × 6) : (R × 18) = 9 : 8 : 11
⇒ 4P : 6Q : 18R = 9 : 8 : 11
Equating individual terms we get,
4P = 9
⇒ P = 9/4
Similarly, Q = 8/6 & R = 11/18
Now, we get,
P : Q : R = 9/4 : 8/6 : 11/18
⇒ P : Q : R = 9/4 × 36 : 8/6 × 36 : 11/18 × 36
⇒ P : Q : R = 81 : 48 : 22
∴ The ratio of their capitals is 81 : 48 : 22.
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