The correct answer is option (E):
neither statement (1) nor statement (2) suffices to answer the question
The question asks for Bakshi's profit share. We're given that Amar, Bakshi, and Chetan invest a total of 24,000 in a business.
Statement 1: The ratio of investments of Amar, Bakshi, and Chetan is 4 : 6 : 9.
This statement tells us the relative proportion of their investments. We can find each person's individual investment using the ratio and the total investment amount. Bakshi's investment would be (6 / (4+6+9)) * 24,000 = (6/19) * 24,000. However, this statement provides information about investments only. We have no information about how these investments translate into profit. We cannot determine Bakshi's profit share. Therefore, Statement 1 alone is insufficient.
Statement 2: Ratio of their profits is equal to the ratio of their investments.
This statement provides the *relationship* between investments and profits. It says that the profit shares are proportional to the investments. But, it does not provide us with the actual investment amounts or the total amount invested. We cannot calculate Bakshi's profit share without knowing the investments or total profit. Therefore, Statement 2 alone is insufficient.
Combining both Statements:
Statement 1 gives us the ratio of investments, and Statement 2 tells us that the profit share is proportional to the investment ratio. Since we know the total investment amount, we can calculate each person's investment based on the ratio given in statement 1. Then, because profits and investments are proportional (Statement 2), we can determine Bakshi's share of the profit.
However, the problem explicitly asks for the profit share, and we do *not* know the total profit. We only know the total investment. To calculate Bakshi's profit share, we need the total profit of the business, which is not provided. Without knowing the total profit, we cannot determine Bakshi's share.
Therefore, neither statement alone nor both statements together are sufficient to answer the question. The correct answer is: neither statement (1) nor statement (2) suffices to answer the question.