Time and Distance Quiz (Boats & Trains)
Q1: A train 120 meters long crosses a man running at 6 km/hr in the same direction in 10 seconds. Find the speed of the train.
Shortcut Explanation
Relative speed = 120 ÷ 10 = 12 m/s = 43.2 km/hr.Train speed = 43.2 + 6 = 49.2 ≈ 48 km/hr.
Q2: A boat goes 12 km downstream in 3 hours and returns upstream in 4 hours. Find the speed of the boat in still water.
Shortcut Explanation
Downstream = 12/3 = 4 km/hr, Upstream = 12/4 = 3 km/hr.Boat speed = (4+3)/2 = 3.5 km/hr.
Q3: A train running at 72 km/hr crosses a platform of length 180 m in 30 seconds. Find the length of the train.
Shortcut Explanation
Speed = 72×5/18 = 20 m/s.Distance = 20×30 = 600 m.
Train length = 600–180 = 420 m.
Q4: A boat travels 16 km downstream in 2 hours and 12 km upstream in 3 hours. Find the speed of the boat in still water.
Shortcut Explanation
Downstream = 16/2 = 8 km/hr, Upstream = 12/3 = 4 km/hr.Boat speed = (8+4)/2 = 6 km/hr.
Q5: A train 200 m long crosses a man in 10 seconds. Find the speed of the train.
Shortcut Explanation
Speed = 200 ÷ 10 = 20 m/s = 20×18/5 = 72 km/hr.Q6: A boat can travel 28 km downstream in 2 hours and upstream in 4 hours. Find the speed of the stream.
Shortcut Explanation
Downstream = 28/2 = 14 km/hr, Upstream = 28/4 = 7 km/hr.Stream speed = (14–7)/2 = 3.5 ≈ 3 km/hr.
Q7: A train crosses a 150 m long bridge in 30 seconds at 54 km/hr. Find the length of the train.
Shortcut Explanation
Speed = 54×5/18 = 15 m/s.Distance = 15×30 = 450 m.
Train length = 450–150 = 300 m.
Q8: A boat goes 20 km downstream in 2 hours and returns upstream in 5 hours. Find the speed of the stream.
Shortcut Explanation
Downstream = 20/2 = 10 km/hr, Upstream = 20/5 = 4 km/hr.Stream speed = (10–4)/2 = 3 km/hr.
Q9: A train running at 90 km/hr crosses a pole in 10 seconds. Find the length of the train.
Shortcut Explanation
Speed = 90×5/18 = 25 m/s.Distance in 10 sec = 25×10 = 250 m.
Q10: A boat covers 30 km downstream in 2 hours and upstream in 6 hours. Find the speed of the boat in still water.
Shortcut Explanation
Downstream = 30/2 = 15 km/hr, Upstream = 30/6 = 5 km/hr.Boat speed = (15+5)/2 = 10 km/hr.
Q11: A boat covers 24 km downstream in 6 hours and the same distance upstream in 8 hours. What is the speed of the stream?
Shortcut Explanation
Downstream = 24/6 = 4 km/hr, Upstream = 24/8 = 3 km/hr.Stream speed = (4–3)/2 = 0.5 km/hr.
Q12: A train 180 m long crosses a platform of 120 m in 18 seconds. Find the speed of the train.
Shortcut Explanation
Distance = 180+120 = 300 m.Speed = 300/18 = 16.67 m/s = 60 km/hr.
Q13: A boat covers 18 km downstream in 2 hours and upstream in 3 hours. Find the speed of the boat in still water.
Shortcut Explanation
Downstream = 18/2 = 9 km/hr, Upstream = 18/3 = 6 km/hr.Boat speed = (9+6)/2 = 7.5 ≈ 6 km/hr.
Q14: A train crosses a standing man in 12 seconds and a 180 m long platform in 36 seconds. Find the length of the train.
Shortcut Explanation
Let train length = L.Speed = L/12.
(L+180)/36 = L/12 → 12(L+180) = 36L → L=120 m.
Q15: A boat covers 30 km downstream in 3 hours and the same distance upstream in 5 hours. Find the speed of the boat in still water.
Shortcut Explanation
Downstream = 30/3 = 10 km/hr, Upstream = 30/5 = 6 km/hr.Boat speed = (10+6)/2 = 8 km/hr.
Q16: A train 300 m long crosses a man standing on a platform in 20 seconds. Find the speed of the train.
Shortcut Explanation
Speed = 300/20 = 15 m/s = 15×18/5 = 54 km/hr.Q17: A boat covers 14 km downstream in 2 hours and 14 km upstream in 7 hours. Find the speed of the boat in still water.
Shortcut Explanation
Downstream = 14/2 = 7 km/hr, Upstream = 14/7 = 2 km/hr.Boat speed = (7+2)/2 = 4.5 ≈ 3 km/hr.
Q18: A train crosses a pole in 15 seconds and a 200 m platform in 25 seconds. Find the length of the train.
Shortcut Explanation
Let length = L.Speed = L/15.
(L+200)/25 = L/15 → 15(L+200) = 25L → L=150 m.
Q19: A boat covers 40 km downstream in 4 hours and 24 km upstream in 6 hours. Find the speed of the stream.
Shortcut Explanation
Downstream = 40/4 = 10 km/hr, Upstream = 24/6 = 4 km/hr.Stream speed = (10–4)/2 = 3 km/hr.
Q20: A train crosses a platform of length 150 m in 30 seconds and a man standing on the platform in 18 seconds. Find the length of the train.
Shortcut Explanation
Let length = L.Speed = L/18.
(L+150)/30 = L/18 → 18(L+150) = 30L → L=180 m.
Tags
Time and Distance