Directions: Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the given question. How much did Rohit get as profit at the year-end in the business done by Nitin, Rohit and Kunal? I. Kunal invested ₹ 8000 for nine months, his profit was $\frac{3}{2}$ times that of Rohit's and his investment was four times that of Nitin. II. Nitin and Rohit invested for one year in the proportion 1 : 2 respectively. III. The three together got ₹ 1000 as profit at the year end.

### Concept & Logic Finding an individual partner's absolute profit requires calculating the profit-sharing ratio for all partners involved (Equivalent Capital = Investment $\times$ Time) and knowing the total absolute profit generated by the business. ### Step-by-Step Solution * **From Statement I:** * Kunal's investment = ₹ $8000$ and Time = $9$ months. * Kunal's investment ($8000$) = $4 \times$ Nitin's investment $\Rightarrow$ Nitin's investment = ₹ $2000$. * This gives us partial data but Rohit's investment and time are missing. * **From Statement II:** * Nitin and Rohit's time = $12$ months. * Ratio of Nitin's investment to Rohit's investment = $1 : 2$. * Using Nitin's investment from Statement I (₹ $2000$), Rohit's investment = ₹ $4000$. * Now we can find the complete equivalent capital ratio (Nitin : Rohit : Kunal) = $(2000 \times 12) : (4000 \times 12) : (8000 \times 9) = 24000 : 48000 : 72000 = 1 : 2 : 3$. * **From Statement III:** * Total profit = ₹ $1000$. * **Combining all three:** With the ratio $1 : 2 : 3$ (from I and II) and the total profit of ₹ $1000$ (from III), Rohit's share is $\frac{2}{6} \times 1000$. * All three statements provide necessary missing pieces to solve the problem. ### Exam Strategy & Shortcut Map the variables needed: $I_N, T_N, I_R, T_R, I_K, T_K$, and Total Profit. Statement I gives $I_K, T_K, I_N$. Statement II gives $T_N, T_R$ and links $I_N$ to $I_R$. Statement III gives the Total Profit. You need all three blocks of information to bridge the gaps and calculate the final figure. ### Common Pitfall Trying to use the condition "his profit was $\frac{3}{2}$ times that of Rohit's" from Statement I to solve the problem without Statement II. While it gives a profit ratio between Kunal and Rohit, we still lack Nitin's profit ratio compared to the others, meaning we cannot distribute the total profit of ₹ $1000$. ### Final Answer Therefore, the correct answer is **All I, II and III**.