A,B,C enter into a partnership ,A invest some amount at the beginning , B invest double the amount of A after 6 month, and C invest thrice the amount of A after 8 months , If the annual profit be 54,000 find the C's ShareQuestion Description : 1800015000900021000
Question
A,B,C enter into a partnership ,A invest some amount at the beginning , B invest double the amount of A after 6 month, and C invest thrice the amount of A after 8 months , If the annual profit be 54,000 find the C's ShareQuestion Description : 1800015000900021000
Solution
The problem is about the distribution of profit in a partnership based on the capital invested and the time for which it was invested.
Let's denote:
- the amount A invested as 'a',
- the amount B invested as '2a' (since it's double the amount of A),
- the amount C invested as '3a' (since it's thrice the amount of A).
The time for which they invested the money also matters. In this case:
- A invested for 12 months,
- B invested for 6 months,
- C invested for 4 months (since it's 12 months - 8 months).
The share of each partner is directly proportional to the product of the money invested and the time period for which it was invested. So, we can write:
- A's share = a * 12,
- B's share = 2a * 6,
- C's share = 3a * 4.
The total profit is 54000. The total share is the sum of A's, B's, and C's shares, which is equal to the total profit. So, we can write:
a * 12 + 2a * 6 + 3a * 4 = 54000.
Solving this equation gives a = 500.
So, C's share in the profit is:
3a * 4 = 3 * 500 * 4 = 6000.
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