Read the following information carefully and answer the given questions. There are ten buses A, B, C, D, E, F, G, H, J, and K which are at the base station. Four platforms P1, P2, P3, and P4 where the first bus can reach at 5 AM, 6 AM, 7 AM, and 8 AM respectively. Platform P1 is the nearest Platform and Platform P4 is the farthest. There must be a gap of one hour between the two buses reaching a particular station. The speed of the buses is considered to be the same. At most three buses can have a platform as its destination. Bus C and D started from the base station and reached the nearest platform in a gap of 1 hour. C started its journey earlier than D. C reached the destination at 6 AM. Bus A stopped its journey at a platform which is two more than Bus D. Bus J reached the last platform. Bus H's destination is not the same as the destination of C, E and K. Destinations of F and G are the same. The destination of F and G is not the same as the destination of D and J. Bus B's destination is the same as the destination of K. There is only one more bus at the platform where Bus J reached its destination. Bus E's final destination is not P1 and P4. Bus B's destination is ahead of Bus E's destination. Which of the following statements is/are false? I. Bus B's destination is P4. II. Bus E and Bus F's destinations are the same. III. Bus D's destination is ahead of Bus F's destination

### Concept & Logical Deduction This is a constraint satisfaction and linear arrangement problem. The key is to deduce the full platform matrix before evaluating the validity of the statements. ### Step-by-Step Solution **1. Understand the Basic Rules:** * 10 Buses across 4 Platforms: P1 (nearest) to P4 (farthest). * Max capacity per platform: 3 buses. **2. Deduce the Final Platform Distribution:** * **P1:** Bus C and D reached the nearest platform. (C, D) * **P3:** A stopped two platforms after D (P1 + 2 = P3). (A) * **P4:** J reached the last platform. P4 has exactly "one more bus" (max 2 total). (J) * **P2 & P3:** B and K go to the same place. B is ahead of E (who cannot be at P1 or P4). B/K cannot be at P4 (would exceed max 2). So B and K must be at P3, making E at P2. * **P2:** F and G go to the same place but not P1 or P4. P3 is full (A, B, K). So F and G are at P2. * **P4:** H is not with C(P1), E(P2), or K(P3). So H is at P4. * **Final Matrix:** P1(C, D), P2(E, F, G), P3(A, B, K), P4(J, H). **3. Evaluate the Statements:** * **Statement I:** Bus B's destination is P4. -> **False** (B is at P3). * **Statement II:** Bus E and Bus F's destinations are the same. -> **True** (Both are at P2). * **Statement III:** Bus D's destination is ahead of Bus F's destination. -> **False** (D is at P1, which is the nearest/starting platform. F is at P2, which is further ahead). Since Statements I and III are false, the correct option is "Only I and III". ### Exam Strategy & Shortcut By mapping the anchors early, you can quickly evaluate options. Recognizing that B is at P3 instantly makes Statement I false, drastically narrowing down the answer choices. ### Common Pitfall Misinterpreting the term "ahead". In linear arrangements starting from a base station, a higher platform number (P2) is physically "ahead" of a lower one (P1) on the route. ### Final Answer Therefore, the correct answer is **Only I and III**.