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A, B, C start a business by investing the capital 5, 6, 8. At the end of business, they receive the profit in the ratio of 5: 3: 12. Find the ratio of time for which they contribute their capital.
Options are:-
5:1:3
3:1:3
2:1:3
4:1:3?
Options are:-
5:1:3
3:1:3
2:1:3
4:1:3?
Most Upvoted Answer
A, B, C start a business by investing the capital 5, 6, 8. At the end ...
Understanding the Problem
To find the ratio of the time for which A, B, and C contributed their capital, we need to analyze their capital investments and the profit distribution.
Capital Investments
- A invests: 5
- B invests: 6
- C invests: 8
Profit Sharing Ratio
- The profit is shared in the ratio: 5:3:12 for A, B, and C respectively.
Calculating Effective Capital Contribution
The profit sharing ratio can be represented in terms of their capital and time. The effective capital contribution can be calculated using the formula:
Effective Contribution = Capital × Time
Let the time for A, B, and C be T_A, T_B, and T_C respectively.
From the profit sharing:
- A's share = 5 × T_A
- B's share = 3 × T_B
- C's share = 12 × T_C
Setting Up the Equations
We can set up the equations based on the profit ratio:
- 5 × T_A = 5k (for some constant k)
- 6 × T_B = 3k
- 8 × T_C = 12k
Now, we can simplify these equations:
- T_A = k
- T_B = 0.5k
- T_C = 1.5k
Finding the Time Ratio
To find the ratio of time:
- T_A : T_B : T_C = k : 0.5k : 1.5k
When we simplify this:
- T_A : T_B : T_C = 1 : 0.5 : 1.5 = 2 : 1 : 3
Final Answer
Thus, the ratio of the time for which A, B, and C contributed their capital is 2:1:3.
To find the ratio of the time for which A, B, and C contributed their capital, we need to analyze their capital investments and the profit distribution.
Capital Investments
- A invests: 5
- B invests: 6
- C invests: 8
Profit Sharing Ratio
- The profit is shared in the ratio: 5:3:12 for A, B, and C respectively.
Calculating Effective Capital Contribution
The profit sharing ratio can be represented in terms of their capital and time. The effective capital contribution can be calculated using the formula:
Effective Contribution = Capital × Time
Let the time for A, B, and C be T_A, T_B, and T_C respectively.
From the profit sharing:
- A's share = 5 × T_A
- B's share = 3 × T_B
- C's share = 12 × T_C
Setting Up the Equations
We can set up the equations based on the profit ratio:
- 5 × T_A = 5k (for some constant k)
- 6 × T_B = 3k
- 8 × T_C = 12k
Now, we can simplify these equations:
- T_A = k
- T_B = 0.5k
- T_C = 1.5k
Finding the Time Ratio
To find the ratio of time:
- T_A : T_B : T_C = k : 0.5k : 1.5k
When we simplify this:
- T_A : T_B : T_C = 1 : 0.5 : 1.5 = 2 : 1 : 3
Final Answer
Thus, the ratio of the time for which A, B, and C contributed their capital is 2:1:3.
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A, B, C start a business by investing the capital 5, 6, 8. At the end of business, they receive the profit in the ratio of 5: 3: 12. Find the ratio of time for which they contribute their capital.Options are:-5:1:33:1:32:1:34:1:3?
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