In a partnership, A invests 1/6 th of the capital for 1/6 th of the time, B invests 1/3 rd of the capital for 1/3 rd of the time and C invests the rest of the capital for the whole time. Out of a profit of $4140, Aandrsquo;s share is:a)$100b)$120c)$180d)$300e)$540Correct answer is option 'C'. Can you explain this answer?

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In a partnership, A invests 1/6 th of the capital for 1/6 th of the time, B invests 1/3 rd of the capital for 1/3 rd of the time and C invests the rest of the capital for the whole time. Out of a profit of $4140, A’s share is:

a)
$100
b)
$120
c)
$180
d)
$300
e)
$540

Correct answer is option 'C'. Can you explain this answer?

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In a partnership, A invests 1/6 th of the capital for 1/6 th of the ti...

Understanding the Investment and Profit Sharing
In this partnership, each partner invests a different amount of capital for different durations. To determine A's share of the profits, we first need to calculate each partner's contribution in terms of "capital-months."
A's Contribution
- A invests 1/6 of the capital for 1/6 of the time.
- Contribution = (1/6) * (1/6) = 1/36 capital-months.
B's Contribution
- B invests 1/3 of the capital for 1/3 of the time.
- Contribution = (1/3) * (1/3) = 1/9 capital-months.
C's Contribution
- C invests the remaining capital.
- Total capital = 1. Thus, C invests 1 - (1/6 + 1/3) = 1/2 of the capital.
- C invests for the whole time (1 time unit).
- Contribution = (1/2) * 1 = 1/2 capital-months.
Total Contributions
- A's contribution = 1/36
- B's contribution = 1/9 = 4/36
- C's contribution = 1/2 = 18/36
Calculating the Shares
- Total contribution = A's + B's + C's = 1/36 + 4/36 + 18/36 = 23/36.
A's Share of the Profit
- A's share of the profit = (A's contribution / Total contribution) * Total profit
- A's share = (1/36) / (23/36) * 4140
- A's share = (1/23) * 4140 = 180.
Conclusion
A's share of the profit is $180, which corresponds to option 'C.'

Answered by Talent Skill Learning · View profile

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