If the circuit is open, i.e. there two ends of the solenoid is open, there is induced emf produced, but no induced current produced. That is why the magnet can fall through normal with free fall acceleration 10 m/s2. Only when the circuit is closed, there is an induced current flowing through. According to Lenz's law, the direction of the induced current is such that the magnetic effect opposses the change producing it, hence there is a repulsion force when the magnet is falling through the solenoid.

Solutions: Option B Without the current in the river, the time taken for the swimmer to reach Q is 50s. This is based on the vertical constant speed of 1.2 m/s and veritcal (width of river) distance. With the current, which is constant 1.0 m/s, the swimmer will be drifted downstream. But the time taken to reach R from P is still 50s. So with the same 50s, you can calculate the horizontal distance based on the horizontal current speed of 1.0 m/s.