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Any partnership in business is based on two components. One is the money or capital that is invested and the other is the time for which the money is invested.
To put mathematically,
Profit is directly proportional to investment and time.
Profit ∝ investment
Profit ∝ time
Profit ∝ investment × time
Hence, any share of profit out of investment is decided by the net effect of these two components.
This net effect is calculated by multiplying money and the duration for which the money is invested.
‘A, B and C entered into a business by investing their intial sum Rs. 12600, Rs. 14400 and Rs. 13200 respectively. After 6 months C left the partnership. B also left the partnership after 8 months. If after a year total profit was Rs. 69600, then find profit share of C.’
Here, instead of taking absolute values of money invested, we may use their simplest values i.e. ratio. Ratio of investment of A, B and C is 21:24:22 respectively.
Ratio of their profit= (21×12):(24×8):(22×6)= 21:16:11
Now, profit share of C= 16/48×69600=15950.
‘Aman started a business investing Rs. 70,000 Rakhi Joined him after six months with an amount of Rs. 1,05,000 and Sagar Joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?’
Ratio of profit is given by the ratio of (investment×time)
Hence, ratio of profit of above three people= (70000×3):(105000×5/2)∶(140000×2)