In each of the following questions, a question is followed by two statements. Read both the statements and find which statements are required to answer the question and answer accordingly. In how many days can A and B together complete a piece of work? Statement I: A alone can complete the same piece of work in 15 days. Statement II: B is 50% more efficient than
A.

From Statement I, we know that A alone can complete the work in 15 days. However, we do not have any information about B's rate of work. So, Statement I alone is not sufficient to answer the question. From Statement II, we know that B is 50% more efficient than A. Or, Ratio of efficiency of A to B = 100 : 150 = 2 : 3 Since no actual time or work is given, we cannot find the number of days. So, Statement II alone is not sufficient to answer the question. From Statement I and II together, we have: ATQ, A's daily work = 1/15 Since B is 50% more efficient than A, B's daily work = 1.5 * (1/15) Or, B's daily work = 1/10 So, daily work of A and B together = 1/15 + 1/10 Or, daily work of A and B together = (2 + 3)/30 = 5/30 = 1/6 So, A and B together can complete the work in 6 days. Thus, both statements together are necessary to answer the question. Hence, the correct answer is E.