Time and Distance problems
- 1. The length of Lucknow mail is 120m and that of punjab mail is 80 m. These two trains are running in the same direction with velocities of 40 km/h and 50 km/h respectively. The time taken by them to cross each other is?
Options- A. 8 sec.
- B. 72 sec.
- C. 11.5 sec.
- D. 12.5 sec. Discuss
Correct Answer: 72 sec.
Explanation:
Relative speed = 50 - 40 = 10 km/h = 50/18 m/s
? Time taken = Sum of length of the trains / Relative speed
= (200/50) x 18 = 72 sec.
- 2. A train passes an electric pole in 10 seconds and a platform 120 m long in 18 seconds. Its length in meters is?
Options- A. 150 m
- B. 130 m
- C. 240 m
- D. 180 m Discuss
Correct Answer: 150 m
Explanation:
Let the length of train be x m, then
x/10 = (120 + x)/18
? x = 150m
- 3. The wheel of an engine of 300 cm in circumference makes 10 revolution in 6 seconds. what is the speed of the wheel (in km/h)?
Options- A. 18
- B. 20
- C. 27
- D. 36 Discuss
Correct Answer: 18
Explanation:
Circumferences means one resolutions .
Therefore, distance covered in 10 resolutions =300 x 10 = 30 m
i.e., 30 meters in 6 seconds.
? Speed of wheel = 30/6 m/s = 5 m/s
? 5 m/s = 5 x (18/5) = 18 km/h
- 4. Anjali fires two bullets from the same place at the interval of 6 minutes but Bhagwat sitting in a car approaching the place of firing hears the second fire 5 min 32 sec after the first firing. What is the speed of car, if the speed of sound is 332 m/s?
Options- A. 56 m/s
- B. 102 m/s
- C. 28 m/s
- D. 32 m/s Discuss
Correct Answer: 28 m/s
Explanation:
(speed of wind) / (speed of car) = (Time utilised) / (time saved)
? 332/x = 332/28
? x = 28 m/s
- 5. A car crosses a man walking at 6 km/h. The man can see the things up to 450m only in one direction due to fog. He sees the car which was going in the same direction for 4.5 minutes. What is the speed of the car?
Options- A. 9 km/h
- B. 12 km/h
- C. 12.5 km/h
- D. 15 km/h Discuss
Correct Answer: 12 km/h
Explanation:
Time = Total distance / Relative speed
4.5/60 hr. = (450/1000) / x
? x = 6 km/h
Relative speed = Speed of car - Speed of man
6 = x - 6
? x = 12 km/h
- 6. X and Y start walking towards each other at 8:00 am at the speeds of 3 km/h and 4 km/h, respectively. They were initially 17.5 km apart. At what time do they meet?
Options- A. 10 : 30 am
- B. 10 : 30 pm
- C. 11 : 30 am
- D. 11 : 30 pm Discuss
Correct Answer: 10 : 30 am
Explanation:
Let they meet after x h.
Then, according to the question,
3x + 4x = 17.5
? 7x = 17.5
? x = 17.5 / 7 = 2.5 h
So, they meet 2.5 h after 8:00 am.
It means they meet at 10:30 am.
- 7. A train leaves manipur at 6:00 am and reaches Dispur at 10:00 am. Another train leaves Dispur at 8:00 am and reaches Manipur at 11:00 am. At what time do the two trains cross each
other?
Options- A. 7 : 56 am
- B. 7 : 56 pm
- C. 8 : 56 am
- D. 8 : 56 Discuss
Correct Answer: 8 : 56 am
Explanation:
Let distance between Manipur and Dispur = D km
Average speed of train from Manipur = D/4 km/h
Average speed of train from Dispur = 2D/7 km/h
Let they meet T h after 6:00 am.
Then, according to the question,
(D/4 x T) + 2D/7 x (T - 2) = D
? T/4 + 2(T - 2)/7 = 1
? 7T + 8(T - 2) = 28
? 15T = 44
? T = 44/15 h = 2h 56 min
Clearly, trains meet 2 h 56 min after 6:00 am.
It means the trains meet at 8:56 am.
- 8. Anurag traveled a distance of 45 km in 8 h 45 min. He traveled partly on foot at 3 km/h and partly by bicycle at 8 km/h .The distance traveled on the bicycle, is?
Options- A. 25 km
- B. 15 km
- C. 30 km
- D. 20 km Discuss
Correct Answer: 30 km
Explanation:
Let the distance traveled on foot be x km
Then, distance converted by bicycle = (45 - x) km
? x/3 + (45 -x) /8 = 83/4 = 35/4
? (8x + 135 - 3x)/24 = 35/4
? 5x + 135 = 210
? 5x = 75
? x = 15
? Distance converted by bicycle = (45 - 15) = 300 km
- 9. Running at a speed of 60 km/h, a train passed through a 1.5 km long tunnel in 2 min. What is the length of the train?
Options- A. 250 m
- B. 500 m
- C. 1000 m
- D. 1500 m Discuss
Correct Answer: 500 m
Explanation:
Suppose length of the train = L m
Speed of the train = 60 km/h = 60 x 1000 = 60000 m/h
Length of tunnel = 1.5 km = 1500 m
Time taken by train = 2 min = 1/30 h
Time = Distance/Speed
? 1/30 = L + 1500/60000
? l = 500 m
- 10. The average speed of a train in the onward journey is 25% more than that of the return journey. The train halts for one hour on reaching the destination. The total time taken for the complete to and fro journey is 17 h covering a distance of 800 km. The speed of the train in the onward journey, is?
Options- A. 45 km/h
- B. 47.06 km/h
- C. 50.00 km/h
- D. 56.25 km/h Discuss
Correct Answer: 56.25 km/h
Explanation:
Let the speed of the train during returning journey be x km/h
Speed during onward journey = x + 25x/100 = 5x/4 km/h.
Distance coverd in onward journey = 800 / 2 = 400 km
Total time taken = Covered distance / Speed
Time taken by train in onward journey = 400/(5x/4)
and time taken in returning journey = 400/x
Thus, 400/(5x/4) + 400/x = 16
? 320/x + 400/x = 16
? 16x = 720
? x = 45 km/h
Speed of the train in the onward journey = 5 x 45/4 = 56.25 km/h
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