How much time will Train P take to cross Train Q (from the moment they meet) running in opposite directions (towards each other)? Statement I: The respective ratio of speeds of Train P and Train Q is 3: 4. The sum of the lengths of Train P and Train Q is 700 meters. Statement II: Train P can cross a signal pole in 12 seconds. It can cross 600-meter long stations in 25 seconds.

Statement II alone gives Train P's length and speed. From crossing a pole in 12s and 600m station in 25s, we can calculate P's length = L_P and speed = S_P. Using the station crossing: (L_P + 600) / S_P = 25, and L_P / S_P = 12, we can solve for both. Statement I gives speed ratio 3:4 and total length 700m. Combined with P's values from II, we get Q's speed and length. After meeting, crossing time = (L_P + L_Q) / (S_P + S_Q). Both statements together are necessary and sufficient.