A’, ‘B’ and ‘C’ started a business by investing Rs. 8,000, Rs. 9,500, and Rs. 7,500, respectively such that ‘B’ invested for 2 months more than ‘C’ and 6 months less than ‘A’. If the ratio of profit share of ‘A’ to the average of profit share of ‘B ‘and ‘C’ together is 50:27, respectively, then find the time for which ‘B’ invested his sum.

According to the question: Let the number of months for which ‘C’ invested his sum = ‘x’ months Then, number of months for which ‘B’ invested his sum = (x + 2) months Number of months for which ‘A’ invested his sum = x + 2 + 6 = (x + 8) months So, the ratio of profit shares of ‘A’, ‘B’, and ‘C’, respectively: = {8000 × (x + 8)}:{9500 × (x + 2)}:{7500 × x} = (8000x + 64000):(9500x + 19000):(7500x) Average of profit share of ‘B’ and ‘C’: = (9500x + 7500x + 19000) ÷ 2 = Rs. (8500x + 9500) According to the question: (8000x + 64000):(8500x + 9500) = 50:27 Or, 50(8500x + 9500) = 27(8000x + 64000) Or, 425000x + 475000 = 216000x + 1728000 Or, 209000x = 1253000 So, x = 6.00 So, the number of months for which ‘B’ invested = x + 2 = 6 + 2 = 8 months