Time, speed and distance
- A car covers 360 km in 6 hours. By how much must its speed be increased to cover the same distance in 4 hours? Answer: C. 30 km/h Answer: (C) 30 km/h Present speed = 360/6 = 60 km/h. Required speed = 360/4 = 90 km/h. Increase = 30 km/h. 1
- A train 180 m long crosses a pole in 9 seconds. How long will it take to cross a platform 270 m long? Answer: B. 22.5 seconds Answer: (B) 22.5 seconds Speed = 180/9 = 20 m/s. To cross the platform it covers 180 + 270 = 450 m: 450/20 = 22.5 s. 1
- Two trains 150 m and 210 m long are running in opposite directions on parallel tracks at 45 km/h and 63 km/h. In how much time will they completely cross each other? Answer: C. 12 seconds Answer: (C) 12 seconds Relative speed (opposite directions) = 45 + 63 = 108 km/h = 108 × 5/18 = 30 m/s. Distance = 150... 1
- Two trains, 150 m and 210 m long, run on parallel tracks in opposite directions at 45 km/h and 63 km/h. How many seconds do they take to cross each other completely? Answer: A. 12 Answer: (A) 12 Relative speed = 108 km/h = 30 m/s. Distance = 150 + 210 = 360 m. Time = 360 ÷ 30 = 12 s. 1
- Walking at 5 km/h, a man reaches his office 10 minutes late. Walking at 6 km/h, he reaches 5 minutes early. What is the distance to his office (in km)? Answer: B. 7.5 Answer: (B) 7.5 The time difference is 15 min = 1/4 h. d/5 - d/6 = d/30 = 1/4 , so d = 7.5 km. 1
- A 240 m long train crosses a pole in 12 seconds. How long (in seconds) will it take to cross a 360 m long platform? Answer: D. 30 Answer: (D) 30 Speed = 240 ÷ 12 = 20 m/s. Distance to cover = 240 + 360 = 600 m. Time = 600 ÷ 20 = 30 s. 1
- A car goes from town P to town Q, 120 km apart, at 40 km/h and returns from Q to P at 60 km/h. What is its average speed for the whole journey (in km/h)? Answer: C. 48 Answer: (C) 48 Time = 120/40 + 120/60 = 3 + 2 = 5 h for 240 km. Average speed = 240 ÷ 5 = 48 km/h. 1
- What is 72 km/h in metres per second? Answer: A. 20 m/s Answer: (A) 20 m/s Multiply by 5/18 : 72 × 5/18 = 20 m/s. 1
- A car covers 360 km in 4 hours 30 minutes. What is its speed? Answer: B. 80 km/h Answer: (B) 80 km/h 4 h 30 min = 4.5 h. Speed = 360 ÷ 4.5 = 80 km/h. 1
- A train 240 m long runs at 54 km/h. How long does it take to pass a signal pole? Answer: D. 16 seconds Answer: (D) 16 seconds 54 km/h = 15 m/s. Time = length ÷ speed = 240 ÷ 15 = 16 seconds. 1
- A train 150 m long running at 72 km/h crosses a platform 250 m long. How long does it take? Answer: D. 20 seconds Answer: (D) 20 seconds Distance = train + platform = 400 m. 72 km/h = 20 m/s. Time = 400 ÷ 20 = 20 seconds. Trap: 7.5... 1
- A man walks at 5 km/h for 3 hours and then at 6 km/h for 2 hours. What is his average speed for the whole walk? Answer: C. 5.4 km/h Answer: (C) 5.4 km/h Total distance = 15 + 12 = 27 km in 5 hours. Average speed = 27 ÷ 5 = 5.4 km/h. Trap: 5.5 is the pl... 1
- Two trains 120 m and 130 m long run in opposite directions at 40 km/h and 50 km/h. How long do they take to cross each other completely? Answer: A. 10 seconds Answer: (A) 10 seconds Opposite directions: relative speed = 90 km/h = 25 m/s. Distance = 120 + 130 = 250 m. Time = 25... 1
- The speeds of A and B are in the ratio 3 : 4. What is the ratio of the times they take to cover the same distance? Answer: D. 4 : 3 Answer: (D) 4 : 3 For a fixed distance, time is inversely proportional to speed. Time ratio = 4 : 3. 1
- A car covers a distance in 3 hours at 40 km/h. At what speed must it travel to cover the same distance in 2 hours 30 minutes? Answer: C. 48 km/h Answer: (C) 48 km/h Distance = 40 × 3 = 120 km. Speed = 120 ÷ 2.5 = 48 km/h. 1
- Walking at \(\frac{3}{4}\) of his usual speed, a man reaches his office 20 minutes late. What is his usual time to reach the office? Answer: A. 60 minutes Answer: (A) 60 minutes At 3/4 the speed he takes 4/3 the time. The extra 1/3 of the usual time = 20 min. Usual time =... 1
- A boy walking at 5 km/h reaches school 7 minutes late. Walking at 6 km/h he reaches 5 minutes early. How far is the school? Answer: C. 6 km Answer: (C) 6 km The difference in time = 7 + 5 = 12 min = 1/5 h. Shortcut: d = S₁ S₂/S₂ - S₁ × time difference = 5 × 6/1 ×... 1
- A train passes a pole in 15 seconds and a 100 m long platform in 25 seconds. What is the length of the train? Answer: B. 150 m Answer: (B) 150 m The extra 100 m (platform) takes 25 − 15 = 10 s, so speed = 10 m/s. Length = 10 × 15 = 150 m. 1
- Two trains 140 m and 160 m long run on parallel tracks in the same direction at 60 km/h and 42 km/h. How long will the faster train take to pass the slower one completely? Answer: D. 60 seconds Answer: (D) 60 seconds Same direction: relative speed = 60 − 42 = 18 km/h = 5 m/s. Distance = 140 + 160 = 300 m. Time... 1
- A policeman is 150 m behind a thief. The thief runs at 8 km/h and the policeman chases him at 10 km/h. How far will the thief have run before he is caught? Answer: B. 600 m Answer: (B) 600 m The gap closes at 2 km/h. Time = 0.15 ÷ 2 = 0.075 h. Thief's distance = 8 × 0.075 = 0.6 km = 600 m. Short... 1
- Two cars start at the same time from towns A and B, 360 km apart, and move towards each other at 50 km/h and 40 km/h. How far from A do they meet? Answer: D. 200 km Answer: (D) 200 km Time to meet = 360 ÷ (50 + 40) = 4 h. The car from A covers 50 × 4 = 200 km. 1
- A man covers three equal distances at 10 km/h, 20 km/h and 60 km/h. What is his average speed for the whole journey? Answer: B. 18 km/h Answer: (B) 18 km/h Take each distance = 60 km (LCM). Times = 6 h + 3 h + 1 h = 10 h for 180 km. Average speed = 180 ÷ 10... 1
- If a person walks at 15 km/h instead of 12 km/h, he would walk 18 km more in the same time. What distance did he actually walk? Answer: B. 72 km Answer: (B) 72 km The extra 3 km/h gives 18 km more, so the time = 18 ÷ 3 = 6 h. Actual distance = 12 × 6 = 72 km. Trap: 90... 1
- A car goes from P to Q at 60 km/h and returns at 40 km/h. The whole trip takes 5 hours. What is the distance from P to Q? Answer: C. 120 km Answer: (C) 120 km Average speed = 2 × 60 × 40/100 = 48 km/h. Total distance = 48 × 5 = 240 km. One way = 240 ÷ 2 = 120 km... 1