X, Y, and Z entered into a partnership with initial investments of Rs. (M + 2500), Rs. 3M, and Rs. (4M - 20000), respectively. After 6 months, W joined the partnership with 70% of the combined investment of Y and Z. At the end of one year, the total profit was Rs. 162500, and W's profit share was 25% less than that of Y. Quantity I: Find the initial investment made by
X. Quantity II: Find 30% of the initial investment of of Y. Quantity III: Find 50% of the initial investment made by W.

Solution

According to the question, Initial investment made by W = 70% (3M + 4M - 20000) = 4.9M - 14000 Ratio of profit share = [(M + 2500) x 2]: [3M x 2]: [(4M - 20000) x 2]: (4.9M - 14000) = (2M + 5000): (6M): (8M - 40000): (4.9M - 14000) W's profit is 25% less than Y's, so 6M / (4.9M - 14000) = 4/3 (18M) = 19.6M - 42000 Thus, the value of M = 42000/1.6 M = 26,250 Quantity I: Initial investment of X = (26,250 + 2500) = Rs. 28,750 Quantity II: 30% of the initial investment of of Y = 0.3*3M = 23,625 Quantity III: 50% of the initial investment made by W = 50% of (4.9 x 26,250 – 14000)  = Rs. 57,312.5 Conclusion: Quantity III  > Quantity I > Quantity II  Hence, the answer is option A.