The question consists of two statements numbered “I and II” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. P, Q and R entered into a business with certain amount of initial investments. After one year, they made additional investments of certain amount. If total profit earned at the end of 2 years is Rs. 8640, then find the profit share of Q. Statement I: Initial investment made by P, Q and R is Rs. 960, Rs. 1200 and Rs. 1440 respectively and after one year they made additional investment in the ratio of 31:35:39 respectively. Statement II: Initial investment made by P, Q and R are in the ratio of 4:5:6 respectively and after 1 year they made additional investment of Rs. (x + 180), Rs. (x + 260) and Rs. (x + 340) respectively.

Statement I: Let additional investment made by P, Q and R be Rs. 31a, Rs. 35a and Rs. 39a respectively. Ratio of profit share of P, Q and R = [960 × 2 + 31a]:[1200 × 2 + 35a]:[1440 × 2 + 39a] = (1920 + 31a):(2400 + 35a):(2880 + 39a) Profit share of Q = (2400 + 35a)/(7200 + 105a) × 8640 So, data in statement I alone is not sufficient to answer the question. Statement II: Let initial investment made by P, Q and R is Rs. 4y, Rs. 5y and Rs. 6y respectively. Ratio of profit share of P, Q and R = [4y × 2 + x + 180]:[5y × 2 + x + 260]:[6y × 2 + x + 340] = (x + 8y + 180):(x + 10y + 260):(x + 12y + 340) Profit share of Q = (x + 10y + 260)/(3x + 30y + 780) × 8640 So, data in statement II alone is not sufficient to answer the question. Combining statement I and II: (x + 180)/(x + 260) = 31/35 35x + 6300 = 31x + 8060 4x = 1760 x = 440 Ratio of profit share of P, Q and R = [960 × 2 + 620]:[1200 × 2 + 700]:[1440 × 2 + 780] = 2540:3100:3660 = 127:155:183 So the profit share of Q = 155/(127 + 155 + 183) × 8640 = Rs. 2880 So data in statements I and II together are necessary to answer the question.