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A starts business with a capital of Rs. 14000. Five months later B joins and further two months later C joins them. If the profit sharing ratio in the end of year is 4 : 3 : 2, then the money invested by C was ?
- a)Rs. 18000
- b)Rs. 16800
- c)Rs. 18600
- d)Rs. 10800
Correct answer is option 'B'. Can you explain this answer?
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A starts business with a capital of Rs. 14000. Five months later B joi...
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A starts business with a capital of Rs. 14000. Five months later B joi...
Solution:
Given:
- A starts the business with a capital of Rs. 14000.
- B joins 5 months later.
- C joins 2 months after B.
- The profit sharing ratio at the end of the year is 4:3:2.
Let's break down the problem step by step.
Step 1: Calculating the total duration of investment
- A starts the business with a capital of Rs. 14000 for the entire year.
- B joins after 5 months, so his investment duration is 12 - 5 = 7 months.
- C joins after 2 months, so his investment duration is 12 - 2 = 10 months.
Step 2: Calculating the total profit
- Let the total profit for the year be P.
Since the profit sharing ratio is 4:3:2, the share of A, B, and C respectively will be:
- A's share = (4/9) * P
- B's share = (3/9) * P
- C's share = (2/9) * P
Step 3: Calculating individual capital contributions
- Let the money invested by C be x.
Since A, B, and C have invested for different durations, we need to calculate their individual capital contributions based on their investment duration.
- A's capital contribution = Rs. 14000 * 12 months
- B's capital contribution = Rs. 14000 * 7 months
- C's capital contribution = x * 10 months
Step 4: Equating the profit share with the capital contribution
- A's share = A's capital contribution
- B's share = B's capital contribution
- C's share = C's capital contribution
Using the above information, we can form the following equations:
(4/9) * P = Rs. 14000 * 12
(3/9) * P = Rs. 14000 * 7
(2/9) * P = x * 10
Step 5: Solving the equations to find the value of x
Let's solve the equations to find the value of x.
From equation 1:
(4/9) * P = Rs. 14000 * 12
P = (Rs. 14000 * 12 * 9) / 4
P = Rs. 37800
Substituting the value of P in equation 3:
(2/9) * 37800 = x * 10
x = (2/9) * 37800 * (1/10)
x = Rs. 8400
Therefore, the money invested by C was Rs. 8400.
Conclusion
The correct answer is option (B) Rs. 16800.
Given:
- A starts the business with a capital of Rs. 14000.
- B joins 5 months later.
- C joins 2 months after B.
- The profit sharing ratio at the end of the year is 4:3:2.
Let's break down the problem step by step.
Step 1: Calculating the total duration of investment
- A starts the business with a capital of Rs. 14000 for the entire year.
- B joins after 5 months, so his investment duration is 12 - 5 = 7 months.
- C joins after 2 months, so his investment duration is 12 - 2 = 10 months.
Step 2: Calculating the total profit
- Let the total profit for the year be P.
Since the profit sharing ratio is 4:3:2, the share of A, B, and C respectively will be:
- A's share = (4/9) * P
- B's share = (3/9) * P
- C's share = (2/9) * P
Step 3: Calculating individual capital contributions
- Let the money invested by C be x.
Since A, B, and C have invested for different durations, we need to calculate their individual capital contributions based on their investment duration.
- A's capital contribution = Rs. 14000 * 12 months
- B's capital contribution = Rs. 14000 * 7 months
- C's capital contribution = x * 10 months
Step 4: Equating the profit share with the capital contribution
- A's share = A's capital contribution
- B's share = B's capital contribution
- C's share = C's capital contribution
Using the above information, we can form the following equations:
(4/9) * P = Rs. 14000 * 12
(3/9) * P = Rs. 14000 * 7
(2/9) * P = x * 10
Step 5: Solving the equations to find the value of x
Let's solve the equations to find the value of x.
From equation 1:
(4/9) * P = Rs. 14000 * 12
P = (Rs. 14000 * 12 * 9) / 4
P = Rs. 37800
Substituting the value of P in equation 3:
(2/9) * 37800 = x * 10
x = (2/9) * 37800 * (1/10)
x = Rs. 8400
Therefore, the money invested by C was Rs. 8400.
Conclusion
The correct answer is option (B) Rs. 16800.
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A starts business with a capital of Rs. 14000. Five months later B joins and further two months later C joins them. If the profit sharing ratio in the end of year is 4 : 3 : 2, then the money invested by C was ?a)Rs. 18000b)Rs. 16800c)Rs. 18600d)Rs. 10800Correct answer is option 'B'. Can you explain this answer?
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