Question
Raj, Sam, and Tina began a business with initial
investments in the ratio 6:5:4 respectively. After one year, Tina, Raj, and Sam made additional investments in the ratio 2:3:1 respectively. Raj is the active working partner, so 30% of the profit is given to him for managing the business, and the rest is distributed among them in the ratio of their investments. Find the profit share of Raj out of the total profit of Rs. 2,500 after two years.Solution
According to the question: Initial investments of Raj, Sam, and Tina: Rs. 6x, Rs. 5x, and Rs. 4x respectively. Additional investments of Tina, Raj, and Sam: Rs. 2y, Rs. 3y, and Rs. y respectively. Ratio of their profits: (6x + 3y):(5x + y):(4x + 2y) = (9x + 3y):(6x + y):(8x + 2y) Profit share of Raj for being an active working partner = 0.30 × 2500 = Rs. 750 Profit share of Raj for his investment = 0.70 × 2500 × (9x + 3y)/(23x + 6y) = Rs. 750 Total amount of profit received by Raj = 750 + 750 = Rs. 1500
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