Which of the following statement is correct? I. Speed of a boat in still water…

Concept

These are two independent kinematics claims judged on standard relative-speed rules. (1) In stream problems, downstream speed = (boat + current) and upstream speed = (boat - current), so the current is found from the downstream excess over still water. (2) When two bodies leave the same point in the SAME direction and one overtakes ("catches") the other, it is a catch-up problem: relative speed = difference of the two speeds, and catch-up time = head-start distance / relative speed.

Statement I - apply

1. Given: speed in still water = 8 km/hr, downstream speed = 12 km/hr.

2. Current = downstream - still water = 12 - 8 = 4 km/hr.

3. Upstream speed = still water - current = 8 - 4 = 4 km/hr.

4. The statement claims 10 km/hr, but the value is 4 km/hr, so Statement I is FALSE.

Statement II - apply

1. A and B leave the SAME point P and B moves towards (chases) A, so this is a catch-up case, not a head-on meeting.

2. A starts at 8 a.m. at 50 km/hr; by 10 a.m. (when B starts) A is ahead by 2 x 50 = 100 km.

3. B chases at 75 km/hr, so the relative (gap-closing) speed = 75 - 50 = 25 km/hr.

4. Catch-up time = 100 / 25 = 4 hr, so B catches A at 10 a.m. + 4 hr = 2 p.m.

5. This matches the claim, so Statement II is TRUE.

Cross-check

• Position check: at 2 p.m. A has run 8 a.m. to 2 p.m. = 6 hr x 50 = 300 km; B has run 10 a.m. to 2 p.m. = 4 hr x 75 = 300 km. Both are 300 km from P, so they coincide - this confirms 2 p.m.

• Common trap: reading "towards A" as opposite directions gives relative speed 125 km/hr and 10:48 a.m.; but both start from the SAME point, so it is a chase, not a head-on approach.

Result

Statement I is false and Statement II is true, so the correct choice is the one stating that only statement II is correct.