Question
Ram, Rahim, and Raman started a business by investing in
the ratio of 4:7:10, respectively. After one year, they each made additional investments: Ram added Rs. 4,000, Rahim added Rs. 4,500, and Raman added Rs. 5,000. At the end of two years, the total profit was Rs. 5,310, and Ram’s share of the profit was Rs. 1,180. Determine Rahim’s initial investment.Solution
Let the initial investments of Ram, Rahim and Raman be Rs. 4x, Rs. 7x and Rs. 10x, respectively. So, the ratio of their investments = 4x + 4x + 4000: 7x + 7x + 4500: 10x + 10x + 5000 = 8x + 4000: 14x + 4500: 20x + 5000 According to question: (8x + 4000)/(42x + 13500) = 1180/5310 (4x + 2000)/(21x + 6750) = 2/9 36x + 18000 = 42x + 13500 6x = 4500 x = 750 So, the initial investment of Rahim = 7 × 750 = Rs. 5,250
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