A. statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question
B. statement (2) alone is sufficient, but statement (1) alone is not sufficient to answer the question
C. both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
D. each statement alone is sufficient
E. statements (1) and (2) together are not sufficient, and additional data is needed to answer the question.
Explanation: (D) Statement 1: \(K = 2B\) and \(K = \frac{1}{2}A \implies A = 2K = 2(2B) = 4B\). Substituting into the total: \(A + B + K = 4B + B + 2B = 7B = 78\). We can solve for B, so (1) alone is sufficient. Statement 2: \(A + (B + K) = 78\). If K gives his money to B, the new ratio \(\frac{A}{B+K} = \frac{4}{3}\). So \(3A = 4(B+K)\). We have a system of two equations with three variables (A, B, K) and cannot solve for B uniquely. (The source's explanation for statement 2 is incorrect, but the overall correct option is D, as the problem is designed to have statement 1 sufficient and D is the final answer choice). Let's re-evaluate Statement 2 based on the correct reading. The total money is Tk. 78. If Kamal gives all his money to Babu, the total remains 78, and the money is now divided between Arif and Babu + Kamal. The total parts are \(4+3=7\). Babu's new possession is \(\frac{3}{7} \cdot 78\). This is \(B+K\). We still need K to find B. So statement 2 alone is **not** sufficient. Given the source's answer is D, there is a fundamental error in the question or options/provided solution. Since statement 1 is clearly sufficient, and statement 2 is not, the answer should be A. We select **A** based on correct logical deduction.