All MCQs

Downstream speed is 15 km/h and upstream speed is 10 km/h.
Still-water speed is their average: 12.5 km/h.

Upstream speed equals still-water speed minus stream speed.
Thus, 10 - 2 = 8 km/h.

Downstream speed equals still-water speed plus stream speed.
Thus, 12 + 3 = 15 km/h.

Relative speed is 66 km/h = 55/3 m/s.
Length = speed × time = 55/3 × 18 = 330 meters.

Total distance is 100 + 140 = 240 meters.
Relative speed is 10 + 14 = 24 m/s, so time = 10 seconds.

The train covers its length plus the platform length: 300 meters.
Speed = 300 ÷ 20 = 15 m/s.

To pass a pole, the train covers its own length.
Speed = 150 ÷ 10 = 15 m/s.

For motion in the same direction, relative speed is the difference.
Thus, 80 - 55 = 25 km/h.

For opposite directions, relative speeds are added.
Thus, 50 + 70 = 120 km/h.

For equal time intervals, average speed is the arithmetic mean.
Thus, (40 + 60)/2 = 50 km/h.

For equal distances, average speed is the harmonic mean 2ab/(a + b).
Thus, 2 × 40 × 60 ÷ 100 = 48 km/h.

Time equals distance divided by speed.
Thus, 12 ÷ 4 = 3 hours.