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. What is the difference in the shares of profit between P and Q in a joint business at the end of one year? (M.B.A., 2007) I. P invested ₹ 80000 and withdrew ₹ 20000 after 6 months. II. Q joined four months after the start of business. III. Q's amount was $80\%$ of P's amount during the last six months.

### Concept & Logic To find an absolute monetary difference between two profit shares, you must have the total profit amount (or one absolute profit amount) in addition to the profit sharing ratio. ### Step-by-Step Solution * **From Statement I:** P's equivalent capital = $(80000 \times 6) + (60000 \times 6) = 480000 + 360000 = 840000$. * **From Statement II:** Q was in the business for $12 - 4 = 8$ months. * **From Statement III:** P's amount in the last 6 months was $60000$. Q's investment = $80\%$ of $60000 = 48000$. * **Combining all:** Q's equivalent capital = $48000 \times 8 = 384000$. * We can now find the ratio of P's share to Q's share (which is $840000 : 384000 = 35 : 16$). * However, we only have the ratio. Neither the question nor the statements provide the **total profit** earned at the end of the year. Without an absolute profit figure, the exact monetary difference cannot be determined. ### Exam Strategy & Shortcut Before doing any heavy arithmetic to find the ratio, quickly scan the question and statements for a total profit value. Since "difference in the shares of profit" requires an absolute value, and no absolute profit value is given anywhere, the data is automatically insufficient. ### Common Pitfall Calculating the entire ratio perfectly but forgetting that a ratio cannot provide an absolute difference without a total amount to anchor it. ### Final Answer Therefore, the correct answer is **Even with all I, II and III together, the answer cannot be arrived at.**